Global high-resolution estimates of the UN Human Development Index using satellite imagery and machine learning

Domain: chemistry
Published: 2026-02-17
Editorial outcome: major_revision

Abstract
The United Nations Human Development Index, which incorporates income, education and health, is arguably the most widely used alternative to gross domestic product. However, official country-resolution estimates (N=191) limit its use. We build on recent advances in machine learning and satellite imagery to produce and distribute global estimates of the Human Development Index for municipalities (N=61,530) and a 0.1°×0.1° grid (N=819,309). To construct these estimates, we develop and validate a generalizable downscaling technique based on satellite imagery that allows for training and prediction with observations of arbitrary size and shape. We show how our estimates can improve decision-making and that more than half of the global population was previously assigned to the incorrect Human Development Index quintile within each country due to aggregation bias. We publish the satellite features necessary to increase the spatial resolution of any other administrative data that is detectable via imagery.

Introduction
The Human Development Index (HDI) is widely used by policymakers and academics to summarize three key dimensions of wellbeing: the population’s health, human capital, and standard of living1–4. A more comprehensive measure of wellbeing than income or wealth alone2,3,5, HDI is used to categorize countries by their level of human development, which, in turn, can determine allocations of global resources6. However, the United Nations Development Program (UNDP) releases official global estimates of HDI annually only at the highly aggregated national level (N=191), preventing the use of the indicator in applications that require subnational information. Thus, measures of income remain the dominant metric for evaluating development progress within countries, in part because they are more readily available.

In an effort to address this, non-UN researchers7 recently processed extensive household survey data in order to produce HDI estimates for first-level administrative units – i.e., provinces and states, hereafter called “provinces” (N=1739). These efforts have substantially advanced our understanding of global development patterns, but province-level measures nonetheless remain too coarse for many modern policy applications where local information is needed, such as community-level targeting of aid8,9. Furthermore, the reliance of current HDI estimates on slow, infrequent, and costly ground-based data collection limits the usability of HDI for most practical applications other than cross-national rankings.

The combination of satellite imagery and machine learning (SIML) is increasingly used to predict socioeconomic variables at fine spatial resolution10–18. This approach enables information that is expensive to obtain through ground surveys to be estimated at low cost. While SIML estimates do not replicate ground surveys exactly19–21, the quality of SIML estimates is now high enough that it can assist targeting of aid and program evaluation in remote communities where alternative sources of information are unavailable8,10,20,22,23.

Here, we produce global estimates of HDI at the second administrative level – i.e., municipalities and counties, hereafter called “municipalities” (N=61,530) and for a global 0.1°×0.1° (approximately 10km by 10km) grid. We construct these estimates by combining information from prior provincial estimates2 with global daytime and nighttime satellite imagery24,25. Our approach builds on recent advances in machine learning12,26 to develop a general method that learns the relationship between imagery and an outcome of interest (here, HDI) using data from any set of political boundaries. We can then use that relationship to estimate the outcome for any other set of boundaries. Importantly, our method works for spatial units of arbitrary shape and size, so models can be trained on coarse-resolution outcome measurements and make predictions at finer resolution. We apply this method to transform provincial HDI measures into finer resolution estimates. While other such “downscaling” approaches typically rely on either theoretically informed relationships or simple dasymetric masks27,28 our approach to making predictions at finer resolution than the source labels uses machine learning and satellite imagery to identify complex spatial relationships between imagery and an outcome of interest (Fig. 1).

Results
Our results have six sections. First, we outline the theoretical approach to downscaling. Second, we train and evaluate a global model for HDI at the province-level using aggregates of satellite features. Third, we implement multiple tests to validate that this model is skillful. Fourth we examine performance for the components of HDI separately. Fifth, we generate high-resolution global HDI data using this procedure, and we evaluate how these estimates compare to existing aggregated estimates. Finally, we illustrate how these high-resolution estimates could alter decision-making when targeting aid.

1. A general approach to downscaling administrative data using satellite imagery and machine learning
The ability of SIML systems to promote development is limited by the paucity of suitable observations for model training10. This limitation is partly due to the design of modern SIML methods, since large quantities of administrative data are available, but existing systems are generally not designed to make use of them. To date, SIML approaches for predicting human outcomes have standardized the structure of both the training labels and corresponding imagery so that the unit of analysis is a regular spatial structure, such as a square. For example, many systems use convolutional neural networks (CNNs)11,13,16, which tend to perform well on diverse computer vision tasks. CNNs, however, typically require images to be a constant size and shape, such as 224 x 224 x 3 pixels in the case of the commonly used ResNet-1829. This restriction has caused prior studies to rely on coarse approximations for linking irregularly shaped labels to corresponding imagery, for example, by averaging polygon labels that overlap with the square image12,14. Such procedures can introduce considerable error when administrative polygons are much larger or smaller than the chosen square size. This is particularly relevant for HDI, for which data is globally available only for nations or provinces, which tend to be irregularly shaped and vary greatly in spatial extent. For example, the largest provincial polygon in our data is the Far Eastern Federal District of Russia, which is over 6 million km2, and the smallest is Banjul of Gambia, which is 7 km2. Developing a robust and widely applicable SIML system that can be trained on inputs that correspond with such diverse administrative structures requires an alternative strategy.

In an ideal setting, we would solve for a function that could directly map a single satellite image “tile” (e.g., 1km × 1km) to the corresponding HDI for the same tile

HDI_tile = f(satellite_image_tile) + \epsilon_tile (1)

where \epsilon_tile is the component of HDI that is not measurable with imagery.

In theory, Eq. (1) could be solved directly with many learning approaches, such as a CNN30, but this is infeasible in practice because tile-level data on HDI (i.e., the left-hand side of Eq. (1), HDI_tile) does not exist. Instead, we observe only aggregated estimates of HDI over politically-defined regions (HDI_country or HDI_province) that correspond with large and irregular agglomerations of image tiles. For the SIML system described by f(⋅), this creates a mismatch between the spatial structure of inputs (image tiles) and outputs (administrative regions).

We solve this problem by converting image tiles into a generalizable set of descriptive variables or “features,” X_tile, such that f(⋅) can be structured as linear in these features,

f(satellite_image_tile) = \beta ⋅ X_tile, (2)

where \beta is a vector of weights (i.e., coefficients). Specifically, we construct a basis for the imagery such that outcomes of interest are well-represented by linear combinations of the basis vectors. This allows aggregate administrative measures of HDI to project onto corresponding aggregations of tile-level features with the same weights that would be recovered if the problem had been solved using only tile-level data. Thus, we learn the model

HDI_province = \beta ⋅ (1/N_province * \sum_{i \in province} X_tile_i) + \epsilon_province (3)

and recover the same weights \beta that we would have recovered had we directly solved Eq. (1) using the linearization in Eq. (2). See Supplementary Information S4 for an empirical validation of the scale-invariance of model weights using this approach. Note that X_province is simply the vector of average tile-level features within a province. The weights \beta can then be used to generate predictions for arbitrary aggregations of tiles. We use these \beta to downscale HDI to the municipality level (\beta ⋅ X_municipality = HDI_municipality) and the tile level (\beta ⋅ X_tile = HDI_tile).

The benefits of linearizing this problem have been understood in general terms, since linear models of basic scalar image properties (e.g., “greenness"31 or nighttime lights32) have been widely used to downscale administrative-level data. However, to our knowledge, it has not been shown that such linearization is possible and skillful for the types of featurization that capture complex spatial structures in imagery.

Here we demonstrate that such a skillful linearization can be achieved by embedding rich image information using the Multi-task Observation using Satellite Imagery and Kitchen Sinks (MOSAIKS) approach12. Converting images into MOSAIKS features (daytime_satellite_image → X_MOSAIKS) provides a structured representation of the unstructured information within the satellite image that performs well in linear models. These features summarize the joint distribution of color and textures within daytime tri-band optical imagery (see “Methods” 1 and Figure S1). We concatenate these features with features that summarize nighttime lights of locations33,34 (nighttime_satellite_image → X_NL) to construct a linear model that downscales HDI using only satellite data (see Methods 4, 5 and 6).

2. Predicting province-level HDI using satellite imagery
Using province-level administrative HDI data for training (as in Equation (3) and Fig. 1), we find that predictions made using linear aggregates of daytime and nighttime satellite image features, anchored to known country means, explain 96% of the variation in global provincial HDI values (Fig. 2A, denoted “full variation performance”). Specifically, we train a model to predict provincial HDI deviations from each country mean and then add the known country mean to the predicted provincial deviations. We take this “mean-anchored” approach, because it reflects how SIML may be used to augment existing HDI data in practice (see “Methods” 9 and Supplementary Information S6.1 for a discussion of mean-anchoring). Since most HDI variation is across-countries rather than within-countries (Fig. 2A, B), much of this performance predicting provincial variation is driven by the measured country means that the predictions are anchored to.

The primary value of incorporating satellite imagery is to explain local-scale variation in HDI. As a first test of the model’s ability to explain local variation, we evaluate model performance predicting deviations in provincial HDI from the country mean. We find that model predictions explain 52% of this within-country provincial variation in HDI (Fig. 2B; see “Methods” 7 for a discussion of performance metrics). This indicates that SIML-based provincial predictions of HDI add substantial fine-resolution information to existing national measures. Importantly, models trained on provincial deviations from the country-level HDI have higher performance predicting such deviations than models trained directly on the provincial values themselves (Table S1 col. 4). Intuitively, model weights are optimized to explain the smaller within-country variation in the demeaned model, rather than the larger across-country deviations (Fig. 2A, B). We use such “within-country” models as our primary model specification.

3. Validating downscaled estimates
We use our downscaling technique to produce estimates at the municipality level and the 0.1°×0.1° grid level, where such estimates have not been previously constructed. Nonetheless, we test the performance of our downscaling technique in three ways that allow predictions to be directly compared to “ground truth” at finer resolution than the training data. First, we directly compare our municipality-level HDI predictions to census-derived estimates in three countries where these data are available: Indonesia, Brazil, and Mexico9,35,36. Second, we train a model relating satellite imagery to the International Wealth Index (IWI) at the province level, and then construct downscaled predictions of IWI at the resolution of Demographic and Health Surveys (DHS) clusters where granular IWI measurements are available37. The IWI is an alternative development indicator to HDI that omits measures of education and health. Third, we train a model to predict nighttime lights (NL), a common proxy for economic wellbeing33,38–43, using features constructed exclusively from daytime satellite imagery, and test whether our approach can downscale NL. Mirroring the structure of our HDI analysis, we train a model using only NL labels aggregated to the province level, and then evaluate predictions of NL at the municipality level. Note that we cannot directly validate the performance for downscaling HDI globally, since the data necessary for such a test do not exist; however, all three of these large-scale tests taken together document the effectiveness of our downscaling strategy in general (using global socioeconomic data similar to HDI) and for HDI in particular (using municipal HDI data for three countries).

When evaluating estimates made at finer resolution than that of the training data, we mean-anchor downscaled estimates to the known provincial mean. This approach produces the best possible estimates by using the satellite-based model to explain within-province variation, which is previously unknown, and the known provincial values to explain the across-province variation.

As a direct evaluation of HDI downscaling performance, we compare municipal HDI predictions from the satellite-based model trained on provincial HDI deviations from the country mean to municipal HDI derived from census-based calculations in Mexico9, Brazil36, and Indonesia35 (Methods 2). In Mexico, downscaled HDI predictions explain 45% of the municipal HDI variation overall (Fig. 2C) and 29% of the within-province variation (Fig. 2D). In Brazil, HDI predictions explain 48% of municipal HDI variation overall, and 20% of the within-province variation. And in Indonesia, HDI predictions explain 61% of the municipal HDI variation overall and 53% of the within-province variation. It is encouraging that HDI predictions align better with census-based measures for Indonesia than for Mexico or Brazil because measures for Indonesia are from 2019, which aligns with our satellite-based predictions of within-province HDI variation, while measures for Mexico and Brazil are from 2010. These older HDI measures could differ from our satellite-based predictions in part due to changes in HDI since the measurements were taken. Additionally, some portion of the misalignment between satellite-based predictions and survey estimates likely arises as a result of errors in the survey data itself, a widely recognized issue10 that we are unable to assess. Together, these results indicate that our method for SIML-based downscaling improves our understanding of the spatial distribution of HDI in these three example countries. We emphasize that these data are not a complete substitute for survey-based estimates and that our model could not be trained or evaluated without ground-truth surveys.

We test the ability of our approach to downscale IWI internationally by training a model on province-level aggregates of IWI and then predicting IWI across DHS clusters. This is a more difficult task than predicting municipality-level values and an equally difficult task as predicting at the 0.1°×0.1° grid-level, since DHS clusters tend to be even finer resolution than municipalities and about the same size as the HDI grid (DHS cluster ≈ 180 km2, municipality ≈ 2000 km2, grid tile ≈ 120 km2). Models are trained on 862 provincial observations within 85 countries and evaluated at 51,996 DHS clusters (Table S1). Analogous to our approach with HDI, models are trained on province-level deviations from country-level means and predictions are re-centered to match the observed province-level mean, as these values are known (see “Methods” S6.2). Downscaled IWI predictions explain 67% of the variation in IWI across all DHS clusters (Fig. 2E) and 56% of the variation in IWI across DHS clusters within countries (i.e., of cluster deviations from the country mean, Fig. 2F). Importantly, this approach is also able to predict 36% of the variation in IWI within the provincial units that it was trained on (Fig. 2G). This result demonstrates the ability of our downscaling approach to generate skillful global-scale predictions at resolutions higher than the training data, and also its ability generalize to measures other than HDI.

To further evaluate our approach in a global test, we train a model on aggregate provincial NL and evaluate predictions at municipal resolution. NL are not a direct measure of human welfare; however, they are generally correlated with income and other development indicators39–41,44,45. NL have even been used along with population to construct development indicators correlated with HDI (e.g., 42). NL are particularly useful here because they allow us to design a validation test where true subnational values are known worldwide. Mirroring our HDI process, we train the model using provincial deviations from the country mean, and then construct municipal values as the predicted municipal deviations from the country mean plus the known country mean (Methods S6.3). Downscaled NL predictions capture 70% of municipal variation in NL globally (Fig. 2H), 63% of the municipal variation within countries (Fig. 2I), and, most importantly, 57% of the variation across municipalities within provinces (Fig. 2J). These results further reinforce the ability of our approach to downscale global province-level data and underscore its generalizability to other non-HDI outcomes. Unlike the two downscaling experiments above, this experiment relies entirely on features generated using only daytime imagery (Figure S2).

Comparisons to municipal data on HDI, IWI, and NL indicate that models trained on provincial data can explain 20-57% of within-province municipal variation. Collectively, these three experiments demonstrate that our approach effectively combines coarse socioeconomic measurements with satellite data to produce skillful estimates at spatial resolutions finer than the province-level training data.

4. Additional evaluation of model performance
One motivation for using MOSAIKS features to downscale HDI is their ability to predict a diversity of ground-based measures. This is particularly relevant for predicting HDI, since it is constructed from components that capture human health, education, and income. To consider which components of HDI are best captured by our estimates, we train models to predict each component of HDI separately. We find that MOSAIKS models explain 92% (5%) of the full (within-country) variation in provincial life expectancy, 93% (51%) of mean years of schooling, 90% (27%) of expected years of schooling, and 97% (56%) of gross national income per capita (GNIpc) (Table S3). While the components of HDI do tend to be correlated (Table S4), these results indicate that instead of just capturing income, predictions of HDI using satellite imagery maintain the ability to capture multiple dimensions of human wellbeing. These results also help explain what aspects of human development satellite features are able to capture, indicating their ability to explain local variation in education and income as well as their difficulty predicting aspects of health. Predictions of HDI made from combinations of its individually predicted components perform nearly identically to the direct predictions of HDI used throughout this analysis.

Further model evaluation including model performance across global regions, and the value of combining daytime and nighttime imagery are discussed in Supplementary Information S2. While it remains untestable how accurately the approach can downscale HDI globally, we find that the approach can predict substantial global variation in HDI and its components, and that it can downscale both HDI in three countries and variables related to HDI globally with accuracy.

5. Global municipality-level and grid-level estimates of HDI
We use our model for within-country HDI (from Results Sections 2–3) to estimate HDI in 2019 for 61,530 municipalities and 819,309 0.1°×0.1° grid tiles (Fig. 3), the finest resolutions at which HDI has been estimated globally (Methods 10). We make these municipal and grid-level estimates of HDI publicly available for download at mosaiks.org/hdi. We also similarly produce and make available estimates of the individual components of HDI.

Our high-resolution estimates enable a substantially more detailed understanding of human development compared with national and provincial measures (Fig. 3A, B vs. C, D). Both municipal and grid-level estimates reveal within-province heterogeneity of HDI that was previously un-resolved (Figures S3, S4). The gridded HDI estimates tend to be higher along major roadways, especially at the intersection of roadways (Figure S5). Borders, such as between Turkey, Georgia, Armenia, Azerbaijan, Iraq and Iran, are less apparent in the fine resolution estimates, indicating a greater continuity in human development across space than in the provincial maps. Higher HDI levels in the city centers and lower HDI levels in the suburbs of capital cities such as Moscow, Russia and Antananarivo, Madagascar are also visible in the municipal and grid estimates, but obscured in the provincial estimates. The contribution of environmental features to human development is illustrated in eastern Pakistan and northwestern India, where human development is higher in the plains bordering the Indus River and its tributaries, and lower in neighboring deserts. Similarly, within Sonora and Sinaloa in Mexico, coastal areas show higher human development than inland regions. This local heterogeneity in HDI indicates that uniform assignment of HDI to populations based on their country or province of residence is inaccurate because it group together populations with very different levels of human development.

We use our estimates to quantify the degree of aggregation bias that occurs when using only province-level estimates. Aggregation bias occurs here because small units (i.e., grids or municipalities) are assigned the HDI of a larger unit (i.e., a province), which does not reflect local conditions. For example, a small urban region, where HDI is high, embedded in a province that also contains large, less developed rural areas, will be assigned a HDI level that is too low when provincial measures are used. We quantify how frequently such misassignment occurs within countries by assigning populations to a quintile of HDI within their national HDI distribution based on provincial, municipal, or grid-level estimates. We then evaluate how frequently the province-level estimates agree with the more highly resolved estimates (Fig. 4).

We find that a majority of the global population (58% using municipal estimates and 65% using grid estimates) is assigned to a different within-country HDI quintile than provincial estimates. For example, of the population measured to be in the bottom two HDI quintiles using provincial estimates, 8.5% are reassigned to the top two HDI quintiles using municipal estimates and 12.9% using grid-estimates. Grid-level estimates reveal larger amounts of aggregation bias due to their finer resolution. Based on our grid-level estimates, we estimate that 20.4% (21.0%) of the global population is one quintile lower (higher) than assigned using provincial estimates, and 9.5% (9.3%) are two quintiles lower (higher).

6. Illustrative application: targeting policy in Mexico
To explore how our HDI measures could improve the efficiency of development policies, we conduct an illustrative targeting exercise within Mexico. We simulate how a geographically targeted policy based on provincial vs. municipal HDI data (Fig. 5A, B) might achieve different outcomes, noting that previous work has shown that more spatially granular targeting can produce meaningful welfare gains13,46–49. We study Mexico because “ground truth” estimates of HDI enable us to benchmark performance9.

The use of municipality-level data improves the number of program recipients correctly targeted. Supposing that the program director aims to provide assistance to the 10% of individuals with the lowest HDI, accuracy of program targeting increases by 11.4 percentage points (from 32.3% to 43.7%) when using municipal data (Fig. 5E, assuming the standard deviation of individual HDI within each municipality is 0.1, see “Methods” 11). Use of the municipal data also results in a much greater geographic dispersion of targeted municipalities (Fig. 5C, D). Evaluation of targeting performance using a receiver operating characteristic curve8 gives similar results (Fig. 5F, Methods 11). Replicating this analysis for Indonesia also gives consistent results (Figure S10).

This application illustrates, in a hypothetical scenario, how fine-resolution HDI estimates could improve targeting of resources, even though these fine-resolution estimates are imperfect. Users of these fine-resolution estimates should consider their specific policy context to determine whether these fine-resolution estimates, which explain 29% of the within-province HDI variation in Mexico, 20% in Brazil, and 53% in Indonesia, provides sufficient additional information to be useful in their setting. Moreover, we acknowledge that there exist other datasets that could alternatively be used for wealth- or income-based targeting (e.g., 13). Still, these estimates may be particularly valuable in data poor settings, where traditional data sources such as surveys are less available and reliable10; only about half of the world’s lowest-income countries have conducted a census in the last decade11,22. These estimates may also be useful in cross-country settings where a globally consistent metric of welfare is desired.

Methods
1. Overview
To transform satellite imagery into descriptive features that exhibit high performance in linear models, we build on the recent development of MOSAIKS, an approach that achieves performance competitive with CNNs using an unsupervised image embedding combined with a linear ridge regression model12. The linearity of ridge regression enables the scale invariance of our downscaling approach12. MOSAIKS random convolutional features combined with ridge regression have been shown to be skillful at solving diverse prediction problems—such as forest cover, population, elevation, and house price— using only imagery as inputs and using only a single linear specification. This property makes MOSAIKS a particularly appealing approach for predicting HDI, which is constructed from multiple development indicators. Each MOSAIKS feature for a tile describes the similarity between the satellite image and a smaller patch of imagery, and is calculated as a nonlinear transformation of the image’s pooled convolution with a random sub-image from the sample12,59. For example, a feature whose patch was sampled from a city might inform how urban an image is, while a feature whose patch was sampled from farmland might inform how agricultural an image is. Together, thousands of MOSAIKS features form a basis that can skillfully describe the rich structure contained within large imagery datasets through simple linear combinations of the features. For details on how MOSAIKS captures visual information from satellite imagery see Figure S1, as well as the Methods sections “Theoretical foundations” and “Convolutional random kitchen sinks”, and the Supplementary Information section “Alternative interpretations relating MOSAIKS to kernels and CNNs” of ref. 12.

To compute local HDI via SIML, we transform a dataset of global Planet imagery (≈5m resolution) into a set of 4000 general-purpose MOSAIKS features (X) for 0.01°×0.01° tiles (≈1km × 1km; Fig. 1)24. We supplement these MOSAIKS features with features that flexibly characterize the distribution of nighttime lights in each tile (Methods 5). While past measures of economic and human wellbeing have tended to focus on nighttime lights alone38–43, inclusion of high-resolution daytime imagery improves model predictions of HDI, especially in regions with low HDI (Supplementary Information S2). Visual imagery may improve performance by better resolving HDI variation in areas without electrification that are nearly dark, or by better differentiating between highly populated areas with lower HDI and less populated areas with higher HDI, which can have similar brightness in night light data16. We then learn a model that is linear in these features (\beta ⋅ X) and use this linear model to estimate HDI at high resolution. While we focus this analysis on the downscaling of HDI, this approach is generalizable to other types of administrative data associated with irregularly-shaped political units.

For both training and prediction, we average image features for administrative polygons using population weights (Fig. 1D, grid-scale predictions follow a similar procedure)60. This results in one vector of image features for each province and municipality in the world. To learn the relationship between the image features and HDI, we train a model on province-level HDI labels and aggregated province-level image features (Fig. 1E). We then predict municipality-level HDI using the municipality-level image features (Fig. 1F), and we predict 0.1°×0.1° grid HDI using features for that grid.

Throughout this analysis we use the term “province", the abbreviation “ADM1” to refer to first-level administrative regions; and “municipality", “ADM2” to refer to second-level administrative regions, though the terminology for these units varies by country. For example, “state" and “county" are the designations used for ADM1 and ADM2 units in the United States.

Our fine-resolution global HDI estimates were produced in collaboration with researchers at the Human Development Report Office of UNDP (Supplementary Information S1), but data released with this paper should not be considered official United Nations indicators.

2. Label data: HDI
The United Nations Human Development Index is a composite measure used to assess a country’s average achievements in three key dimensions of human development: health, education, and standard of living4. Health is measured by life expectancy at birth; education is evaluated using a combination of mean years of schooling for adults and expected years of schooling for children; and standard of living is assessed through gross national income per capita (GNIpc), adjusted for purchasing power parity. The HDI applies a logarithmic transformation to GNIpc to account for the diminishing benefits of increased income. Each of these components is normalized on a scale from 0 to 1, and the HDI is calculated as the geometric mean of the three dimension indices, giving equal weight to each dimension. This method allows the HDI to reflect not just economic wealth, but also broader aspects of well-being. In 2019, the average HDI across countries was 0.72, with a standard deviation of 0.15, a minimum of 0.36 in Somalia and a maximum of 0.96 in Switzerland. (Fig. 3A).

National-level HDI data originate from the UNDP Human Development Data Center and are updated every year61. UNDP uses data from the World Bank, UNESCO, UNICEF, DHS, UN Stats, and other organizations to create these national-level indicators4.

Province-level data on HDI and its components, as well as the associated provincial shapefile, come from the Global Data Lab (GDL) Subnational HDI Database V7.07,62. We omit 3% of the observations, which do not match with the associated GDL shapefile. The resulting province-level HDI dataset contains 1739 provincial observations from 159 countries. Additionally, we include 20 country-level observations that do not have subnational province units (e.g., Qatar). For all model training and evaluation we use provincial HDI data from 2019, the same year as the MOSAIKS image features.

We compare our municipal HDI estimates with census-derived municipal estimates for HDI, where these data exist. For Indonesia, time series estimates of HDI at the municipality level are made publicly available by Badan Pusat Statistik (BPS), the statistics agency of Indonesia63. We use estimates from 2019, which makes these, to our knowledge, the only available municipal HDI data that come from the same year as our satellite imagery.

For Brazil, the Human Development Report Office of the United Nations Development Program has derived HDI data at the municipality level using census data36. The most recent year these data are available is 2010, which we use in this analysis. The census-derived data have a different mean than the 2019 HDI data that we use elsewhere in this analysis; though, this has no influence on the within-country or within-province evaluation metrics (Fig. 2C, D) because predictions and observations are demeaned at the country and province level, respectively, before the metrics are calculated.

For Mexico, census derived estimates of HDI are available for the year 2010, constructed by ref. 9. As with Brazil, these data have a different mean than the 2019 HDI data; though, again, that has no influence on the within-country or within-province evaluation metrics (Fig. 2C, D).

When certain components of HDI are not directly available at the municipal level, producers of these datasets use close proxies. For example the BPS calculates municipal HDI data in Indonesia using data on real expenditure rather than GNIpc35. And when calculating municipal HDI in Mexico, ref. 9 use the child survival rate rather than life expectancy at birth for the health index and an asset index rather than GNIpc for the standard of living index. Likewise, provincial HDI estimates are also constructed using proxies when direct measurements of HDI components are not available7. Discrepancies in how HDI is calculated at the municipal and provincial levels may contribute to differences between our satellite-based HDI estimates and these survey-based HDI estimates.

3. Label data: IWI
IWI data also come from GDL. These data are publicly available at the country and province levels and we use these data for 2019. GDL also provided us IWI data at the DHS cluster level, which are not publicly available. We use cluster-level IWI estimates from 2012 through 2019 in this analysis. We drop observations that do not overlap a parent province polygon and for which no imagery is available. This results in 51,996 DHS cluster observations from 41 countries.

We match all label data to time-constant satellite image features from 2019. Because these features are not contemporaneous with all labels, our results present a conservative estimate of the ability of SIML to measure HDI globally. Given that HDI variation is substantially larger over space than time, however, perfectly contemporaneous measures would likely improve performance only modestly.

4. MOSAIKS features
We create daytime image features using Planet’s Surface Reflectance Basemaps product from 2019, which has a pixel resolution of 4.77m × 4.77m at the equator. These quarterly mosaics are processed by Planet to minimize cloud cover, balance color across seasons, and remove seams from images24,25. We used data from quarter 3 because it corresponds with less ice coverage in the northern hemisphere and less cloud cover in the tropics. We follow the methods described in Rolf et al. to generate a set of 4000 task agnostic daytime image features using random convolutional features12,24. Two thousand of these features use a patch size of 4×4×3 pixels, and the other two thousand use a patch size of 6×6×3 pixels. The third dimension of the patch size refers to the number of color bands (i.e., red, green, and blue) that are available in Planet imagery. We selected these patch sizes because they maximized performance across three non-HDI prediction tasks: predicting night light intensity, road length, and forest cover at the global level. We tested patch sizes ranging from 3×3×3 to 10×10×3 and found that using a combination of two different patch sizes (with 2000 patches each) outperformed using a single patch size (with 4000 patches) across all three tasks.

We create features for all land tiles with available imagery on a global 0.01°×0.01° equal-angle grid, amounting to ≈151 million feature vectors in total24. Features become more sparse above 60° latitude, due to a lack of available imagery. Fig. 1C shows individual images spanning 0.01°×0.01°, along with their corresponding MOSAIKS feature values.

We create polygon-level feature vectors by averaging values across the feature tiles associated with each polygon. Each administrative polygon is represented by a single vector of 4000 daytime image features. We assign each feature tile to the administrative polygon that contains its centroid. For small municipal and DHS polygons that do not contain any tile centroids, we represent the polygon by the nearest feature tile. When averaging, we weight by population using data from the Global Human Settlement Layer (GHS-POP)60. We use the GHS-POP data product for the year 2020 at 30 arcsecond (0.008°) resolution.

5. Nighttime light features
We create non-linear NL features from the Visible Infrared Imaging Radiometer Suite (VIIRS) average masked data product33. We use the V2.1 annual composite from the year 2019. The data has global coverage at 15 arcsecond (0.004°) resolution. Radiance units are expressed as nW/cm2/sr. We assign the small number of pixels with negative radiance values to have a value of zero.

We create features that flexibly characterize the distribution of the NL data using indicator variables that represent whether the radiance value of each NL pixel falls into each of 21 bins. The first bin represents radiance values of zero. The next 20 bins represent radiance values that fall into evenly spaced quantiles of the global distribution of positive NL values. Analogous to aggregating the daytime imagery features to the polygon level, we calculate the population-weighted average value for each of the 21 bins for a given polygon. These polygon-level NL features denote the fraction of each polygon’s population that is covered by NL values represented by each of the 21 bins. This approach allows NL to associate non-linearly with the outcome variables in our linear models.

We compute average nighttime light features for polygons by weighting by population in our main analysis. Thus, changes in VIIRS grid cell sizes caused by latitude do not affect these feature values64, since total population in each cell is measured independently of pixel area. We also verify that population-weighted features, which should have higher performance than area-weighted features because HDI is measured on a per-person basis (not per-area) do indeed have higher performance. For within-country provincial performance, R2 = 0.52 using population-weighted features, and R2 = 0.24 using area-weighted features, which were constructed accounting for the change in the VIIRS grid cell size with latitude.

Use of the “average masked" VIIRS data product should generally have background, biomass burning, and aurora radiance removed34. To the extent there is still unmasked flaring in the NL data, we anticipate that the use of population-weighting when constructing the NL features minimizes this bias, as oil producing areas are typically sparsely populated.

6. General model specification
All models are trained at either the country or province level and use either the 4000 MOSAIKS daytime imagery features, the 21 NL features, or both. We train models using a five-fold cross-validation procedure with basic ridge hyper-parameter tuning. Data are split by country during cross-validation to account for spatial autocorrelation and to ensure that the model is predicting provincial outcomes when no observations from within the same country have been observed. We apply a clipping procedure that restricts model predictions to the minimum and maximum value observed in the training data. Hyper-parameter tuning is done with this clipping procedure. We allow for a different hyper-parameter between the MOSAIKS and NL feature sets, though this has only a minor impact on our results.

The general linearized model, representing Eq. (3), that we implement is

Y = \beta_0 + \beta_1 X_MOSAIKS + \beta_2 X_NL + \epsilon (4)

Where Y is used to refer to the HDI, IWI, or NL labels interchangeably. We use this same model but predict each outcome separately. X_MOSAIKS is the matrix of daytime MOSAIKS features and X_NL is the matrix of night light features. We learn \beta_0, \beta_1, and \beta_2 using ridge regression, following Rolf et al.12. When predicting the NL outcome, we always exclude the X_NL feature matrix. For each outcome, we report performance for models trained at the country, province, and within-country levels (Table S1). Model training is further detailed in Supplementary Information S6.1.

7. Performance metrics
For each model specification, we report two metrics, both of which are used in the literature. The coefficient of determination (R2), used to evaluate related models by ref. 13 and others, describes the accuracy of the raw model predictions and is a direct measure of model skill. The square of the correlation coefficient (\rho^2), used by ref. 16 and others, scores performance after allowing model predictions to be linearly rescaled before they are compared to observed values. We calculate both of these metrics when evaluating the full variation in labels and when decomposing the variation in labels into components that are visible within-countries or within-provinces (in contrast to between-countries and between-provinces).

The “full variation” performance metrics describe how well we estimate subnational HDI globally when we use all information available to us. To calculate full variation performance, we calculate \rho^2 and R2 on the predicted and observed values of subnational HDI directly. This evaluates the ability of model predictions to capture the total variation in the observed values – i.e., variation across countries, across provinces within countries, and across municipalities or DHS clusters within provinces. Because most of the variation in HDI and other outcomes is between countries (Fig. 2A, B), a large portion of the model’s full variation performance comes directly from the mean-anchoring procedure (when it is used). Thus, the full variation performance metrics do not precisely evaluate the model’s ability to predict local variation in isolation, and so they are not our preferred evaluation metric for understanding model performance within countries. Instead, we focus our analysis on within-country and, when applicable, within-province performance.

The “within-country” performance measures the amount of variation in the provincial deviations from the country mean that can be explained by the model. This metric evaluates the ability of the model to explain local variation in the outcome by removing large-scale variation in the outcome across countries in the demeaning step before predictions and observations are compared. To calculate within-country performance, we calculate \rho^2 and R2 after demeaning predictions and observed values at the country level (i.e., after subtracting the predicted and observed country average value from each predicted and observed data point, respectively).

The “within-province” performance metric evaluates the ability of the model to explain hyper-local variation in the outcome, such as which DHS clusters within each province have higher or lower IWI. It does this by removing all between-province variation in the predicted and observed values before they are compared. To calculate within-province performance, we calculate \rho^2 and R2 after demeaning predictions and observed values at the province level.

8. Model evaluation
When reporting model performance at the same resolution as training (Fig. 2 top row, Table S1 upper section, and Table S3), we evaluate predictions from the validation folds of a five-fold spatial cross-validation procedure in which models are trained and evaluated on data from non-overlapping sets of countries. This enables more observations to be used when evaluating model performance. We also evaluate models on a held-out test set of countries that were not included when tuning the HDI model. Before analysis, we set aside ≈ 20% of the provincial HDI data to be used as a final evaluation test set by randomly sampling 35 countries and their respective provinces. Evaluation on this test set was conducted after all hyper-parameter tuning and analysis decisions were made. We find that performance is not meaningfully different in the validation and tests sets, which indicates that the models evaluated on the validation folds did not over-fit to the data (Table S2).

In the downscaling experiments, we evaluate performance using fine-resolution municipal or DHS cluster observations that were not used for model training or tuning. After tuning the model using cross-validation we train the model using the optimal hyper-parameters on all the province or country observations before predicting at downscaled resolution.

9. Mean-anchoring
In our primary within-country model, we anchor our estimates to country or province-level means depending on the experiment. Estimates from models trained on provincial or national observations in “levels” (Table S1) are never mean-anchored.

The procedure for anchoring to the country mean is illustrated in the top row of Fig. 2, where we evaluate performance at the same resolution as model training. Our within-country model is trained to predict within-country anomalies, so in order to predict HDI in “levels” (Fig. 2A), we add back the known country average HDI (Equation S2). This procedure enables us to calculate full variation performance (Fig. 2A) but has no impact on the reported within-country performance (Fig. 2B).

In the downscaling application, our goal is to produce the best possible estimates at fine resolution. Thus, when producing downscaled estimates of IWI and HDI, we anchor our predictions to the observed provincial value of the outcome (Equation S8). This re-centering procedure impacts the full variation performance and the within-country performance but does not impact the within-province performance (Table S1). Note that we anchor municipal NL estimates to country means, rather than provincial means, because we find that this improves the estimates (Supplementary Information S6.3). Mean anchoring and model evaluation are further detailed in Supplementary Information S6.1.

10. Producing downscaled estimates of HDI
To produce fine-resolution estimates of HDI, we take the local estimates of HDI that we predict using satellite imagery and mean-anchor them to province-year values from 2019. This approach uses existing provincial values to explain provincial HDI over space and time, and then supplements that with information on local (i.e., within-province) variation in HDI predicted by the satellite imagery.

We use the within-country model specified in Equation S1a to estimate HDI at the municipality level, using a municipality (ADM2) shapefile from geoBoundaries65. We anchor municipality estimates by centering predicted deviations on the observed province-level HDI value for each year, following the procedure for downscaled IWI predictions (Equation S8). We do not release HDI estimates for municipalities that cannot be linked to a parent province with a province-level HDI estimate from Smits and Permanyer7 because there is not a known provincial value to anchor on.

To produce 0.1°× 0.1° estimates of HDI, we similarly use the within-country models specified in Equation S1a. We make predictions using MOSAIKS features at 0.1° × 0.1° resolution. This results in gridded estimates of HDI at approximately 10 km2 resolution. We mask out locations where humans are not believed to be settled based on GHS-POP60 (keeping areas with population >0) and then mean-anchor our tile estimates such that the population-weighted average of the grid tiles within each province matches known provincial HDI values.

11. Targeting applications
In Fig. 5 we evaluate how access to more granular HDI data improves the number of program recipients correctly targeted. We assume the goal is to provide a uniform transfer to those at or below the tenth percentile of the HDI distribution. Following Smythe and Blumenstock (2022)8, the program is geographically targeted and all individuals within targeted regions receive the same transfer, a practice used to reduce administrative costs46,66. If the administrator has access to only provincial HDI measures, then eligibility is determined at the province-level. Alternatively, using our municipal estimates, the administrator is able to target the program at the municipality level.

We evaluate performance using the census-derived municipality-level HDI measurements9—which are not used to train our model. These are the same census-derived measures used to evaluate performance in Fig. 2C, D and discussed above (Methods 2). Because these estimates are municipality-level aggregates, we simulate HDI for individuals—i.e., the targets of the policy—by imposing additional assumptions about the distribution of HDI across individuals within a municipality. We assume HDI within each municipality has a truncated normal distribution (bounded between 0 and 1) that is centered around the census-derived municipality mean (Figure S6).

The degree to which municipal HDI measures improve targeting performance relative to provincial measures depends somewhat on the assumed dispersion of individual HDI values within municipalities. Assuming lower (higher) dispersion lead to larger (smaller) absolute—though similar proportional—gains (Fig. 5E and Figure S6).

When evaluating performance using a receiver operating characteristic curve (ROC), (Fig. 5F) the aim is still to provide assistance to the 10% of individuals with the lowest HDI, but the fraction of the total population targeted is modified to examine how the true positive (individuals with low HDI correctly given aid) and false positive (individuals with HDI above the desired cutoff incorrectly given aid) rates change accordingly. Moving from left to right on the x axis in Fig. 5F implies a greater number of people receiving assistance. The area under the curve (AUC) shows the efficiency of the targeting. The AUC increases by 0.1 (+13% from 0.76 to 0.86) when municipal data are used instead of provincial data, indicating improved targeting performance when the budget constraint is varied.

As an additional robustness check, we repeat this policy targeting experiment using Indonesia municipality data63 and observe a similar increase in AUC under the same assumptions (11% from 0.62 to 0.69). This is shown in Figure S10.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In the article “Global high-resolution estimates of the United Nations Human Development Index using satellite imagery and machine learning,” the authors present a MOSAIKS-based approach to estimate the Human Development Index (HDI) at municipal and grid-level spatial resolutions using satellite imagery. Their methodology involves a downscaling technique that utilizes province-level HDI data to train the model, enabling predictions at finer spatial scales for municipalities of varying shapes and sizes, and also a grid level with 0.1x 0.1 degree.This work aims to address critical gaps in sub-national HDI data, uncovering disparities often overlooked by traditional methods. The study holds potential for bridging global development data gaps, with implications for informed policy-making and equitable resource allocation, particularly in underserved regions, emphasizing the importance of high-resolution HDI estimates. If this paper is accepted, their estimates are likely to be widely used in future research and policy-making, potentially affecting populations influenced by their outcomes. Therefore, this study requires a very high standard of rigor and thorough validation. However, we believe that this article needs significant revisions before publication in Nature Communications. We would like to begin the first round of review by sharing the eight primary concerns. Once these concerns have been adequately addressed, we believe it will be appropriate to proceed with a detailed review of the methods and their specific aspects.\n\n1.1. Comprehensive review on related studies and comparison needed\nAs the author describes in the paper, there have been numerous efforts to measure socio-economic indicators related to the Sustainable Development Goals (SDGs) using satellite imagery. For instance, prior studies have focused on estimating indicators such as Gross Domestic Product (GDP) [1], poverty levels [2], and asset wealth [3]. This paper focuses on the measurement and downscaling of the Human Development Index (HDI), presenting the first global estimates of HDI at the second-level administrative units. However, an additional consideration arises as follows:\nTheir main contribution is the first instance of estimating HDI (and its components) using satellite imagery on a **global** scale. However, there have been several attempts that made a prediction for specific areas, such as country[4] or regional[5] level. [4] measured HDI for county regions corresponding to ADM2 level in China, and [5] measured HDI for the East Java region in Indonesia.\nEspecially, in a prior study [5], a more diverse range of remote sensing data sources was employed to measure HDI, rather than relying solely on MOSAIKS. For example, NDVI (Normalized Difference Vegetation Index), NDWI (Normalized Difference Water Index), and NDBI (Normalized Difference Built-up Index) were derived from Sentinel-2A bands to provide information on vegetation, water, and built-up areas, respectively. Additionally, datasets such as MODIS and Sentinel-5P were utilized. In contrast, the authors of the current paper conducted regression using MOSAIKS combined with VIIRS nightlight imagery, with results presented in Tables S1–S3. Notably, nightlight imagery was the sole baseline used for methodology validation. To enhance the novelty and robustness of their findings, experiments incorporating other globally available remote sensing datasets, such as MODIS or Sentinel, are recommended. Alternatively, the authors should explicitly address why such data were excluded, citing specific limitations such as temporal or spatial resolution constraints.\n[1] Engstrom, R., Hersh, J., & Newhouse, D. (2022). Poverty from space: Using high resolution satellite imagery for estimating economic well-being. The World Bank Economic Review, 36(2), 382-412.\n[2] Jean, N., Burke, M., Xie, M., Davis, W. M., Lobell, D. B., & Ermon, S. (2016). Combining satellite imagery and machine learning to predict poverty. Science, 353(6301), 790-794.\n[3] Yeh, C., Perez, A., Driscoll, A., Azzari, G., Tang, Z., Lobell, D., ... & Burke, M. (2020). Using publicly available satellite imagery and deep learning to understand economic well-being in Africa. Nature communications, 11(1), 2583.\n[4] Zhang, X., Xu, J., Zhong, S., & Wang, Z. (2024). Assessing uneven regional development using nighttime light satellite data and machine learning methods: evidence from county-level improved HDI in China. Land, 13(9), 1524.\n[5] Ramadhan, R., & Wijayanto, A. W. (2023). Integrating Satellite Imageries and Multiple Geospatial Big Data for Granular Mapping of Spatial Distribution of Human Development Index in East Java, Indonesia. In Proceedings of The International Conference on Data Science and Official Statistics (Vol. 2023, No. 1, pp. 274-295).\n\n2.1. Lack of comprehensive validation\nOne of the critical weaknesses of this article is its lack of comprehensive validation for the downscaling methods. Validating the granular-level HDI estimates is crucial, as the approach relies on HDI “estimates” data from first-level administrative units as the primary training dataset. These first-level HDI estimates are not ground-truth data but rather modeled outputs derived from extensive household survey data. Consequently, the secondary estimates generated through this approach require robust and rigorous validation to ensure their reliability and applicability.\nIn Section 2, the authors employ two strategies to validate their method: comparing their HDI estimates with survey data from Mexico and testing their model on two other wealth-related indicators, the International Wealth Index and Nighttime Lights. As computer vision analysts in the satellite imagery domain, we understand the inherent challenges of evaluating grid-level satellite imagery features due to the scarcity of high-resolution ground-truth datasets across diverse countries. However, these two strategies are insufficient to fully establish the credibility of their results and their utility for policy-making.\nFirst, validating the estimates using data from only one country is inadequate. While high-resolution HDI ground-truth data is rare, there are countries that publish components of the HDI at the municipal level, which could enhance the robustness of the validation. For instance, several East Asian countries report ‘years of schooling’ at the municipal level, and many high- income countries (e.g., Canada) publish municipal-level data on life expectancy at birth. While constructing fully comprehensive ground-truth HDI datasets may not be feasible, these individual indicators can serve as valuable proxies for evaluating the model’s performance more comprehensively across different geographic and socioeconomic contexts.\nSecond, we are not fully convinced that testing the model on other wealth-related indicators can provide sufficient theoretical or empirical evidence to validate the model's utility for HDI estimation. While these indicators may correlate with wealth or development, they do not directly measure the multidimensional components of HDI, such as education, life expectancy, and income. As a result, such tests fail to rigorously demonstrate the model's ability to accurately capture the complexities of HDI and its applicability for real-world policy-making.\n\n2.2. Lack of time-series validation\nThe paper appears to validate the estimates from 2012 to 2021 individually by year (Figure S8). However, since the results span from 2012 to 2021, additional validation is needed to assess how well the model captures temporal changes. Specifically, the validation should assess whether the year-to-year variations in the HDI estimates align with actual HDI data. This involves verifying the increases or decreases in HDI over time against reliable ground-truth data to ensure that the model accurately captures temporal trends and dynamics. As previous studies have argued [1], validating time-series changes and temporal predictions from satellite imagery is inherently more challenging than estimating a single time point. For instance, if the performance at a single time point is 0.6, the performance across two time points may decrease due to textual differences between satellite images taken in different years and months.\n\n2.3. Downscaling of the composite HDI index versus individual components\nAnother issue of concern is the (main) manuscript’s methodological focus on downscaling the HDI as a composite index, rather than separately downscaling its individual components and subsequently aggregating them into a single estimate. As evidenced in Table S4 of the manuscript, the components of the HDI demonstrate low correlations and distinct distributions within countries. For example, the Pearson correlation between expected years of schooling and life expectancy is only 0.1. This indicates that treating the HDI as a unified index may obscure critical spatial variations in its underlying dimensions, potentially reducing both the precision and interpretability of the estimates. While the authors provide the performance of their model for each HDI component in the supplementary materials (Table S3), we argue that these results should be elevated to the main manuscript to emphasize their significance and address these methodological concerns.\nAlso, in our view, while the HDI index is meaningful in itself, it is even more important to understand the different forms of development across various dimensions. For instance, even with the same HDI score, one region may exhibit a high education index but low life expectancy, while another may show high income but low education scores. These varying patterns of development require different policy responses. Therefore, we believe that producing granular-scale estimates for each individual component of HDI would be more valuable, as it would allow for targeted interventions.\n[1] Burke M. et al. (2021). Using satellite imagery to understand and promote sustainable development. Science, 371, eabe8628.\n\n3.1. Baseline comparisons\nThe paper assumes that the model predictions explain a fairly significant portion of HDI variations. For example, it reports that model predictions explain 52% of within-country provincial variation in HDI. However, the authors do not discuss whether explaining 52% (or other numbers) of the variation is sufficient to consider the model reliable for policy applications. This omission raises questions about the adequacy of the model's performance for informing HDI-related policies. One key challenge in evaluating this performance is the lack of a baseline comparison with other models capable of estimating HDI or related indices. While there may not be a prior model specifically designed for HDI estimation using satellite imagery and machine learning (SIML), there are existing SIML approaches that could potentially be adapted for HDI prediction. For example, Relative Wealth Index (RWI) in Mexico constructed from Meta [1] can be used for the granular-level baseline comparisons in Table S1. Establishing such a baseline would provide critical context for interpreting the reported performance and determining its practical significance.\n[1] Chi, G., Fang, H., Chatterjee, S., & Blumenstock, J. E. (2022). Microestimates of wealth for all low-and middle-income countries. Proceedings of the National Academy of Sciences, 119(3), e2113658119.\n\n3.2. Ablation study: Excessive Contribution of Nightlight Data to the Full Model’s Performance\nAs described in the ridge regression, MOSAIKS and nightlight are the two primary features used for estimating HDI in a given region. Table S1-S3 showcase the model performance with ablations, where each component is excluded. However, upon reviewing the data in Table S1, it appears that the NL standalone model shows comparable performance to the full model in terms of ρ² and R². In some cases the NL model even overperforms the full model. For example, when predicted at municipality level in Mexico, within-country performance of MOSAIKS+NL presents 0.5 ρ² (0.45 R²) while that of NL is 0.58 ρ² (0.5 R²). In light of these results, the authors are encouraged to provide evidence supporting the meaningful contribution of MOSAIKS in the full model.\n\n4.1. Same weights β for linearization at tile, province, municipality levels.\nThe model assumes that the weights (β) representing the relationship between satellite imagery features and HDI are consistent across different spatial scales, such as tiles, provinces, and municipalities. However, this assumption—that the same β applies regardless of scale—does not appear to have been explicitly validated in this study. Given the differences in spatial aggregation and scale, it is critical to test whether this assumption holds, as it directly impacts the robustness and reliability of the model's estimates.\n\n4.2. Methodological novelty\nAnother methodological issue is the heavy reliance of this study's model on the MOSAIK framework, which was previously published in Nature Communications [1]. While it is noteworthy that this paper applies the approach to estimating different datasets (i.e., HDI) and provides the first global estimates at the second administrative level, it is difficult to identify significant methodological advancements compared to the earlier work. The primary novelty lies in the application context rather than in the development of the modeling approach itself, raising questions about the extent of its contribution beyond the adaptation to a new target variable.\nIf the methodological advancements are not substantial, it raises the question of whether the work would be better suited for publication as a scientific data paper rather than as a full research article. In such a case, the focus should be on rigorously validating the dataset to ensure its credibility and utility for future research and applications, rather than emphasizing methodological innovation.\n[1] Rolf, E. et al. (2021). A generalizable and accessible approach to machine learning with global satellite imagery. Nature Communications, 12(1), 1-11.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "The paper “Global high-resolution estimates of the United Nations Human Development Index using satellite imagery and machine learning” contains the first granular estimates of the UN’s Human Development Index. The paper develops a downscaling technique that uses provincial estimates to generate estimates at a more granular level. The paper is very well- written, to the point, and contains numerous relevant and convincing robustness checks. The authors anticipated and addressed many of my questions related to the interpretability of the model, its performance over time, its performance by HDI dimension, and whether the relationship between the features and the outcome is geographically stable. I have three comments, which I think could help improve the relevance and applicability of the model.\n\n1. Use of multiple imputation techniques.\nThe authors point out that the predictions have a much lower variance than the true distribution, which is also evident from several of the panels of Figure 2. If I am not mistaken, this means that the model systematically underpredicts the extent to which non-poor provinces have poor municipalities, as well as the extent to which poor provinces have non-poor municipalities. This seems to be an important issue given that perhaps the main purpose of the paper (as illustrated with the targeting example in Mexico) is to uncover such situations. Multiple imputation and small area estimation techniques have existed for decades to deal with the issue that the variance of the predicted values is too small. Could the authors use such techniques to recover more plausible predictions? I realize that small area estimation applications predict at the same level as which ground-truth data are available, so the authors are in a different situation here. Yet surely there are some assumptions about the error term one could make to recover more realistic predictions, perhaps utilizing the Mexican data where the true distribution of municipal estimates is available. If not attractive, and no attractive alternative exists, please explain why.\n\n2. Discussion of advantages/disadvantages for targeting relative to alternative approaches\nThe policy relevance of the paper clearly comes from improved within-country targeting of resources, as cross-country targeting of resources tends to rely on country-level data. Yet it is unclear when countries armed with these estimates would use them for targeting resources. Countries with administrative data would probably use those for targeting, while countries with recent census and survey data would probably rely on small-area estimation techniques to generate granular measures of well-being (I realize small area estimation techniques rarely if ever have the HDI on the left-hand side, but they could have any multidimensional measure of well-being that can be recovered from surveys). What are the cases the authors envision the data generated could be applied? Perhaps in countries with no census, no survey data, no admin data? Or do you think this method works better than small-area estimation techniques? If so, what is the evidence to that end? This paper might be of interest for the discussion: https://doi.org/10.1016/j.jdeveco.2024.103352\n\n3. Interpretation of the model’s error\nThe authors conduct numerous different and relevant checks to test the performance of their model. The overarching challenge is that an ideal assessment of the model would require true granular HDI estimates which, except for in one circumstance, do not exist. The one genuine test of the error they can make suggests that the performance is moderate at best (Figure 2D), with an R^2 of 0.29, while the other one that comes close (2G) is likewise not too great. I think the authors ought to place greater emphasis on the point that the model fundamentally cannot be evaluated in a first-best manner and that second-best approximations suggest that one-third of the relevant variance can be predicted by the model.", "reviewer_4": "Summary\nThe manuscript by Sherman et al. presents a novel method to downscale the United Nations Human Development Index (HDI) using a combination of high-resolution daytime and nighttime satellite imagery and machine learning. The study addresses the critical issue of aggregation bias in traditional HDI measurements by demonstrating that a significant fraction of the global population is misclassified when relying solely on country- or province-level data. Validation using survey-based estimates in Mexico and comparisons with alternative socioeconomic indicators (e.g., the International Wealth Index and nighttime lights) support the robustness of the proposed approach. Overall, the work offers a promising avenue to support more spatially precise policymaking and contributes substantially to the literature on satellite-based socioeconomic measurements.\n\nMajor Comments\n1. Introduction:\nThe paper assumes how HDI is constructed at the national and municipal levels, but it would be beneficial to explicitly mention the range of HDI (0 to 1), its variation across countries, and the weights assigned to each component (education, health, and income).\nIn Mexico, municipal-level HDI estimation relies on the population census for education and health, but the income variable is estimated using small area estimation techniques (Elbers, Lanjouw, and Lanjouw 2003). These estimations are inherently uncertain. It would strengthen the paper to contrast the proposed method with these techniques, highlighting not only the limitations of census data for small areas but also the challenges in obtaining statistically valid income estimates at the municipal level.\n\n2. Methodological Clarity:\nWhile the authors discuss the MOSAIKS method, a clearer explanation with a more accessible example would enhance understanding. Figure 1 provides a visual representation, but the role of colors and the integration of socioeconomic variables could be explained more explicitly. A simplified schematic or a step-by-step breakdown of Figure 1 would aid readers unfamiliar with MOSAIKS in grasping how the method links coarse provincial data with fine-resolution predictions.\nThe paper could delve deeper into the comparison between the proposed method and small area estimates (SAE). It would be valuable to discuss whether the ML-based downscaling approach offers advantages over SAE, particularly in terms of variance and accuracy.\nThe paper does not expand on the consistency of estimates in well-being over time. Specifically, it would be insightful to investigate instances where the official HDI shows an increase, while alternative measures like SIML suggest a decrease (or viceversa). Are there such cases?"}, "author_response": "Response to Reviewer Comments for “Global high-resolution estimates of the United Nations Human Development Index using satellite imagery and machine learning”\nReviewer comments in blue italics.\nOur replies in black.\nReviewer #1 (Remarks to the Author):\nIn the article “Global high-resolution estimates of the United Nations Human Development Index using satellite imagery and machine learning,” the authors present a MOSAIKS-based approach to estimate the Human Development Index (HDI) at municipal and grid-level spatial resolutions using satellite imagery. Their methodology involves a downscaling technique that utilizes province-level HDI data to train the model, enabling predictions at finer spatial scales for municipalities of varying shapes and sizes, and also a grid level with 0.1x 0.1 degree.This work aims to address critical gaps in sub-national HDI data, uncovering disparities often overlooked by traditional methods. The study holds potential for bridging global development data gaps, with implications for informed policy-making and equitable resource allocation, particularly in underserved regions, emphasizing the importance of high-resolution HDI estimates. If this paper is accepted, their estimates are likely to be widely used in future research and policy-making, potentially affecting populations influenced by their outcomes. Therefore, this study requires a very high standard of rigor and thorough validation. However, we believe that this article needs significant revisions before publication in Nature Communications. We would like to begin the first round of review by sharing the eight primary concerns. Once these concerns have been adequately addressed, we believe it will be appropriate to proceed with a detailed review of the methods and their specific aspects.\nWe thank the reviewer for their thoughtful and insightful review. Please find our responses to these eight primary concerns below.\n1.1. Comprehensive review on related studies and comparison needed\nAs the author describes in the paper, there have been numerous efforts to measure socio-economic indicators related to the Sustainable Development Goals (SDGs) using satellite imagery. For instance, prior studies have focused on estimating indicators such as Gross Domestic Product (GDP) [1], poverty levels [2], and asset wealth [3]. This paper focuses on the measurement and downscaling of the Human Development Index (HDI), presenting the first global estimates of HDI at the second-level administrative units. However, an additional consideration arises as follows:\nTheir main contribution is the first instance of estimating HDI (and its components) using satellite imagery on a **global** scale. However, there have been several attempts that made a prediction for specific areas, such as country[4] or regional[5] level. [4] measured HDI for county regions corresponding to ADM2 level in China, and [5] measured HDI for the East Java region in Indonesia.\nEspecially, in a prior study [5], a more diverse range of remote sensing data sources was employed to measure HDI, rather than relying solely on MOSAIKS. For example, NDVI (Normalized Difference Vegetation Index), NDWI (Normalized Difference Water Index), and NDBI (Normalized Difference Built-up Index) were derived from Sentinel-2A bands to provide information on vegetation, water, and built-up areas, respectively. Additionally, datasets such as MODIS and Sentinel-5P were utilized. In contrast, the authors of the current paper conducted regression using MOSAIKS combined with VIIRS nightlight imagery, with results presented in Tables S1–S3. Notably, nightlight imagery was the sole baseline used for methodology validation. To enhance the novelty and robustness of their findings, experiments incorporating other globally available remote sensing datasets, such as MODIS or Sentinel, are recommended. Alternatively, the authors should explicitly address why such data were excluded, citing specific limitations such as temporal or spatial resolution constraints.\n[1] Engstrom, R., Hersh, J., & Newhouse, D. (2022). Poverty from space: Using high resolution satellite imagery for estimating economic well-being. The World Bank Economic Review, 36(2), 382-412.\n[2] Jean, N., Burke, M., Xie, M., Davis, W. M., Lobell, D. B., & Ermon, S. (2016). Combining satellite imagery and machine learning to predict poverty. Science, 353(6301), 790-794.\n[3] Yeh, C., Perez, A., Driscoll, A., Azzari, G., Tang, Z., Lobell, D., ... & Burke, M. (2020). Using publicly available satellite imagery and deep learning to understand economic well-being in Africa. Nature communications, 11(1), 2583.\n[4] Zhang, X., Xu, J., Zhong, S., & Wang, Z. (2024). Assessing uneven regional development using nighttime light satellite data and machine learning methods: evidence from county-level improved HDI in China. Land, 13(9), 1524.\n[5] Ramadhan, R., & Wijayanto, A. W. (2023). Integrating Satellite Imageries and Multiple Geospatial Big Data for Granular Mapping of Spatial Distribution of Human Development Index in East Java, Indonesia. In Proceedings of The International Conference on Data Science and Official Statistics (Vol. 2023, No. 1, pp. 274-295).\nWe thank the reviewer for the comment. These referenced contributions are now all cited in the manuscript (e.g., lines 38-39). We especially thank the reviewer for the reference to Ramadhan et al. (2023), which led us to municipality-level HDI data that we were previously unfamiliar with. We use this data to further validate our HDI estimates, as discussed in our response to the reviewer’s second comment below.\nTo address the reviewer’s concern, we now implement the reviewer’s suggestion to incorporate other globally available remote sensing datasets into the analysis. Following Ramadhan et al. (2023), we add three indices that the reviewer suggests (NDVI, NDWI and NDBI from the Sentinel satellite) to our model. We describe this analysis in the discussion on lines 331-344:\nHere, we use satellite imagery due to its rich information content, global availability, and near uniformity in quality across countries. To evaluate whether additional satellite data sources beyond visual daytime imagery and nighttime imagery might improve HDI estimates, we follow ref. (22) and add to the baseline model three additional index-based features constructed from Sentinel-2A satellite imagery that integrate knowledge of spectral properties of different ground conditions: the Normalized Difference Vegetation Index, Normalized Difference Water Index, and Normalized Difference Built-Up Index. We find that the model performance is essentially unchanged (Table S5), indicating that these additional features do not provide additional information beyond what is already captured by the MOSAIKS and NL features. While it is important to note that there is a limit to how well socioeconomic variables can be predicted using satellite imagery generally, and adding these additional features did not improve performance in this case, future work should nonetheless explore whether incorporating additional imagery sources and/or other ancillary data can improve these estimates (52).\nThe new Table S5 is reproduced below:\nBecause the introduction of these additional features did not affect performance, we have chosen to retain the model using MOSAIKS and nighttime light features as our primary specification.\nGiven that the field combining satellite imagery and machine learning is growing rapidly, we nonetheless hope that future research can build upon this approach and the global fine-resolution estimates of HDI it provides.\n2.1. Lack of comprehensive validation\nOne of the critical weaknesses of this article is its lack of comprehensive validation for the downscaling methods. Validating the granular-level HDI estimates is crucial, as the approach relies on HDI “estimates” data from first-level administrative units as the primary training dataset. These first-level HDI estimates are not ground-truth data but rather modeled outputs derived from extensive household survey data. Consequently, the secondary estimates generated through this approach require robust and rigorous validation to ensure their reliability and applicability.\nIn Section 2, the authors employ two strategies to validate their method: comparing their HDI estimates with survey data from Mexico and testing their model on two other wealth-related indicators, the International Wealth Index and Nighttime Lights.\nAs computer vision analysts in the satellite imagery domain, we understand the inherent challenges of evaluating grid-level satellite imagery features due to the scarcity of high-resolution ground-truth datasets across diverse countries. However, these two strategies are insufficient to fully establish the credibility of their results and their utility for policy-making.\nFirst, validating the estimates using data from only one country is inadequate. While high-resolution HDI ground-truth data is rare, there are countries that publish components of the HDI at the municipal level, which could enhance the robustness of the validation. For instance, several East Asian countries report ‘years of schooling’ at the municipal level, and many high-income countries (e.g., Canada) publish municipal-level data on life expectancy at birth. While constructing fully comprehensive ground-truth HDI datasets may not be feasible, these individual indicators can serve as valuable proxies for evaluating the model’s performance more comprehensively across different geographic and socioeconomic contexts.\nSecond, we are not fully convinced that testing the model on other wealth-related indicators can provide sufficient theoretical or empirical evidence to validate the model's utility for HDI estimation. While these indicators may correlate with wealth or development, they do not directly measure the multidimensional components of HDI, such as education, life expectancy, and income. As a result, such tests fail to rigorously demonstrate the model's ability to accurately capture the complexities of HDI and its applicability for real-world policy-making.\nWe thank the reviewer for this suggestion and agree that further validation of the downscaled estimates would build greater confidence in their reliability and applicability. We also agree that the ideal validation exercise would be to compute HDI from survey data from municipalities globally, and then compare that with our remotely sensed estimates of HDI. However, as the reviewer notes, these data do not exist. Nonetheless, in an effort to address the reviewer’s concern, we have obtained two additional large-scale survey-based municipal estimates of HDI for Indonesia and Brazil. We emphasize that identifying and obtaining these data took significant effort; for example, the data from Brazil was obtained through personal contacts at the United Nations Development Programme. The main text now uses these data similarly to how the data from Mexico was previously used. This means we have expanded the population for which we conduct the near-ideal validation from 130 million people (Mexico only) five-fold to 620 million people (adding Brazil and Indonesia). To our knowledge, this now represents the largest dataset of survey-based municipal HDI estimates.\nWe now discuss model performance comparing our satellite-based estimates with these survey-based estimates on lines 159-177:\nDownscaling HDI in Mexico, Brazil and Indonesia\nAs a direct evaluation of HDI downscaling performance, we compare municipal HDI predictions from the satellite-based model trained on provincial HDI deviations from the country mean to municipal HDI derived from census-based calculations in Mexico (9), Brazil (35), and Indonesia (34) (Methods 2.3). In Mexico, downscaled HDI predictions explain 45% of the municipal HDI variation overall (Figure 2C) and 29% of the within-province variation (Figure 2D). In Brazil, HDI predictions explain 48% of municipal HDI variation overall, and 20% of the within-province variation. And in Indonesia, HDI predictions explain 61% of the municipal HDI variation overall and 53% of the within-province variation. It is encouraging that HDI predictions align better with census-based measures for Indonesia than for Mexico or Brazil because measures for Indonesia are from 2019, which aligns with our satellite-based predictions of within-province HDI variation, while measures for Mexico and Brazil are from 2010. These older HDI measures could differ from our satellite-based predictions in part due to changes in HDI since the measurements were taken. Additionally, some portion of the misalignment between satellite-based predictions and survey estimates likely arises as a result of errors in the survey data itself, a widely recognized issue (15) that we are unable to assess. Together, these results indicate that our method for SIML-based downscaling improves our understanding of the spatial distribution of HDI in these three example countries; although, it is not a complete substitute for survey-based estimates when such data are available.\nWe have also now added Brazil and Indonesia to the second row of Figure 2, where previously we only plotted data from Mexico:\nThese new results are also now reported in Table S1, which has been modified to accommodate the additional analysis:\nThe new data from Indonesia and Brazil are now described in the methods section on lines 493-518:\n2.3 Municipality-level HDI\nWe compare our municipal HDI estimates with census-derived municipal estimates for HDI, where these data exist.\nIndonesia Time series estimates of HDI at the municipality level are made publicly available by Badan Pusat Statistik (BPS), the statistics agency of Indonesia (63). We use estimates from 2019, which makes these, to our knowledge, the only available municipal HDI data that come from the same year as our satellite imagery.\nBrazil The Human Development Report Office office of the United Nations Development Programme has derived HDI data at the municipality level for Brazil, using census data (35). The most recent year these data are available is 2010, which we use in this analysis. The census-derived data have a different mean than the 2019 HDI data that we use elsewhere in this analysis; though, this has no influence on the within-country or within-province evaluation metrics (Figure 2 C,D) because predictions and observations are demeaned at the country and province level, respectively, before the metrics are calculated.\nMexico Census derived estimates of HDI are also available in Mexico for the year 2010, constructed by ref. (9). As with Brazil, these data have a different mean than the 2019 HDI data; though, again, that has no influence on the within-country or within-province evaluation metrics.\nWhen certain components of HDI are not directly available at the municipal level, producers of these datasets use close proxies. For example the BPS calculates municipal HDI data in Indonesia using data on real expenditure rather than GNIpc (34). And when calculating municipal HDI in Mexico, ref. (9) use the child survival rate rather than life expectancy at birth for the health index and an asset index rather than GNIpc for the standard of living index. Likewise, provincial HDI estimates are also constructed using proxies when direct measurements of HDI components are not available (7). Discrepancies in how HDI is calculated at the municipal and provincial levels may contribute to differences between our satellite-based HDI estimates and these survey-based HDI estimates.\nThese direct validations of the downscaling approach using observations of subnational HDI from Mexico, and now Indonesia and Brazil as well, reinforce the additional downscaling tests applying the method to nighttime lights and the IWI. In all tests, the approach is able to predict substantial variation in municipal HDI, or related wealth indices, within the provincial units on which the model was trained. This, in combination with the rest of the paper’s analyses, provides substantial evidence that the downscaling approach provides new and useful information on HDI at fine resolution globally.\nWe also agree with the reviewer that IWI and NL differ in important ways from HDI. In the text we write that: “The IWI is an alternative development indicator to HDI that omits measures of education and health.” (lines 144-145). And clarify that NL is “a common proxy for economic wellbeing” (line 146).\nNonetheless, to avoid any confusion with readers, we also now clarify (lines 149-153) that:\nNo test can directly validate the performance for downscaling HDI globally, since the data necessary for such a test do not exist; however, all three of these large-scale tests taken together document the effectiveness of our downscaling strategy in general -- using global socioeconomic data similar to HDI -- and for HDI in particular -- using municipal HDI data for three countries.\nConsidering our validation exercises together, the provincial tests show that the approach can predict HDI (Fig 2 A-B), as well its components (Table S3), at global scale. The IWI and NL tests show that the approach can downscale socioeconomic indicators similar to, but not the same as, HDI at regional to global scale (Fig 2 E-J). And the municipal HDI tests show that the approach can downscale HDI for three large countries. Thus, we now additionally clarify that (lines 235-238):\nWhile it remains untestable how accurately the approach can downscale HDI globally, we find that the approach can predict substantial global variation in HDI and its components, and that it can downscale both HDI in three countries and variables related to HDI globally with accuracy.\nWe thank the reviewer for encouraging us to identify and obtain these additional validation data, as it was a major effort that we would not have otherwise undertaken and we believe that it substantially strengthens our findings and the quality of the analysis.\n2.2. Lack of time-series validation\nThe paper appears to validate the estimates from 2012 to 2021 individually by year (Figure S8). However, since the results span from 2012 to 2021, additional validation is needed to assess how well the model captures temporal changes. Specifically, the validation should assess whether the year-to-year variations in the HDI estimates align with actual HDI data. This involves verifying the increases or decreases in HDI over time against reliable ground-truth data to ensure that the model accurately captures temporal trends and dynamics. As previous studies have argued [1], validating time-series changes and temporal predictions from satellite imagery is inherently more challenging than estimating a single time point. For instance, if the performance at a single time point is 0.6, the performance across two time points may decrease due to textual differences between satellite images taken in different years and months.\nThank you for this comment; we agree with the reviewer’s assessment that throughout the literature, changes over time tend to be more difficult to predict using satellite imagery than changes over space. Like the reviewer, we are interested in time-series changes in much of our research; however, we focus this manuscript on estimating fine-resolution spatial variation in HDI because existing provincial measures do not resolve within-province differences in human wellbeing, and because spatial variation in HDI is generally 60 times larger than temporal variation.\nNonetheless, as described in Methods Section 4.5, we construct fine-resolution global estimates of HDI from 2012-2021 by adding time-constant satellite-based estimates of municipal HDI deviations from the provincial mean onto time-varying survey-based provincial values over this temporal range. That is, we use the satellite imagery to downscale annual first level administrative HDI estimates to higher spatial resolution, but do not predict or evaluate changes in the within-province distribution of HDI over time (lines 683-685):\nThis approach assumes that the spatial pattern of HDI within provinces does not change over time; relaxing this assumption gives similar results (Supplementary Information S3).\nSupplementary Information Section S3 provides further discussion of and analysis on this topic (lines 1076 - 1090):\nWe focus this manuscript on estimating fine-resolution spatial variation in HDI because existing provincial measures do not resolve within-province differences in human wellbeing, and because spatial variation in HDI is generally larger than temporal variation. We construct fine-resolution global estimates of HDI from 2012-2021 by combining time-varying estimates of provincial HDI from (7) with time-constant estimates of the local (i.e. within-province) distribution of HDI based on satellite imagery. Here, we conduct an additional experiment where we test whether allowing HDI to vary over time locally might improve model performance. Specifically, we compare our primary estimates (Figures 2 A-B and S8 A-B), which are made assuming a time-constant distribution of provincial HDI with another set of estimates that are made allowing for a time-varying distribution of provincial HDI (Figure S8 C-D). We find that these two approaches have near identical performance predicting historical HDI from 2012-2021. This motivates our use of the simpler model that assumes an approximately time-constant distribution of HDI as our primary specification when constructing municipal and grid-level estimates. Details of this analysis are described below…\nTo further clarify this for readers we have now updated our discussion of this topic in the conclusion to read (lines 371-381):\nWe have produced global downscaled estimates of HDI for 2012-2021 by combining existing provincial measures with fine-resolution satellite estimates. This approach estimates municipal HDI in each year by adding satellite-based estimates of municipal HDI deviations from the provincial mean, which are time-constant, onto time-varying provincial values calculated from surveys (7). These municipal values are appropriate for applications comparing levels of HDI across locations within a specific moment in time. They cannot be used to evaluate changes in the distribution of HDI within-provinces over time. Current data does not allow us to distinguish performance between our validated approach and an approach that estimates local trends in HDI (Figure S8 and Supplementary Information S3). Developing additional approaches for tracking and validating subnational trends in HDI is an important area for future research.\n2.3. Downscaling of the composite HDI index versus individual components\nAnother issue of concern is the (main) manuscript’s methodological focus on downscaling the HDI as a composite index, rather than separately downscaling its individual components and subsequently aggregating them into a single estimate. As evidenced in Table S4 of the manuscript, the components of the HDI demonstrate low correlations and distinct distributions within countries. For example, the Pearson correlation between expected years of schooling and life expectancy is only 0.1. This indicates that treating the HDI as a unified index may obscure critical spatial variations in its underlying dimensions, potentially reducing both the precision and interpretability of the estimates. While the authors provide the performance of their model for each HDI component in the supplementary materials (Table S3), we argue that these results should be elevated to the main manuscript to emphasize their significance and address these methodological concerns.\nAlso, in our view, while the HDI index is meaningful in itself, it is even more important to understand the different forms of development across various dimensions. For instance, even with the same HDI score, one region may exhibit a high education index but low life expectancy, while another may show high income but low education scores. These varying patterns of development require different policy responses. Therefore, we believe that producing granular-scale estimates for each individual component of HDI would be more valuable, as it would allow for targeted interventions.\n[1] Burke M. et al. (2021). Using satellite imagery to understand and promote sustainable development. Science, 371, eabe8628.\nTo address the reviewer’s concern, we have followed the reviewer’s suggestion and moved the discussion of Table S3 into the main text on lines 217-238.\nAs suggested by the reviewer, we also now create and release data for Mean Years Schooling, Expected Years Schooling, Life Expectancy and GNIpc, using an approach identical to that for HDI. This is now described on lines 244-245:\nWe also similarly produce and make available estimates of the individual components of HDI.\nWe also shared the reviewer’s intuition that modeling and predicting each HDI component separately and then calculating HDI could potentially improve model performance. However, when we try this, we find that it produces nearly identical results, which is consistent with some prior theoretical results on how MOSAIKS works (12). We now report this result on lines 230-232:\nPredictions of HDI made from combinations of its individually predicted components perform nearly identically to the direct predictions of HDI used throughout this analysis.\n3.1. Baseline comparisons\nThe paper assumes that the model predictions explain a fairly significant portion of HDI variations. For example, it reports that model predictions explain 52% of within-country provincial variation in HDI. However, the authors do not discuss whether explaining 52% (or other numbers) of the variation is sufficient to consider the model reliable for policy applications. This omission raises questions about the adequacy of the model's performance for informing HDI-related policies. One key challenge in evaluating this performance is the lack of a baseline comparison with other models capable of estimating HDI or related indices. While there may not be a prior model specifically designed for HDI estimation using satellite imagery and machine learning (SIML), there are existing SIML approaches that could potentially be adapted for HDI prediction. For example, Relative Wealth Index (RWI) in Mexico constructed from Meta [1] can be used for the granular-level baseline comparisons in Table S1. Establishing such a baseline would provide critical context for interpreting the reported performance and determining its practical significance.\n[1] Chi, G., Fang, H., Chatterjee, S., & Blumenstock, J. E. (2022). Microestimates of wealth for all low-and middle-income countries. Proceedings of the National Academy of Sciences, 119(3), e2113658119.\nThank you for this thoughtful comment. In our original manuscript, the example policy application in Mexico was designed to test and illustrate how the data we generate could provide actionable information to a policy-maker. We have now expanded this demonstration to Indonesia, building on the micro-data discussed above. In addition, to further clarify key issues raised by the reviewer, we have now added a more general discussion of the utility of our fine-resolution HDI estimates alongside our illustrative application of HDI-based geographic targeting for a policy on lines 297-308:\nThis application illustrates how fine-resolution HDI estimates can improve targeting of policies that would otherwise use coarser provincial measures, even though these fine-resolution estimates are imperfect. Using provincial measures implicitly assumes no within-provincial variation in HDI, so any positive ability to predict variation within provinces improves understanding of the spatial distribution of HDI. Users of these fine-resolution estimates should consider their specific policy context to determine whether these fine-resolution estimates, which explain 29% of the within-province HDI variation in Mexico, 20% in Brazil, and 53% in Indonesia, provide sufficient additional information to be useful in their setting. These estimates may be particularly valuable in data poor settings, where traditional data sources such as surveys are less available and reliable (15); only about half of the world’s poorest countries have conducted a census in the last decade (16, 26). These estimates may also be useful in cross-country settings where a consistent metric of welfare is desired.\nWe also agree that understanding the performance of our approach relative to other potential approaches for predicting global HDI at fine resolution is valuable, while also acknowledging that a first global fine-resolution estimate is useful and can serve as a platform for future improvements. We cannot directly apply the approach in Chi et al., (2022) to predict HDI using our data because their approach uses regularly structured data of similar shapes and sizes, and because fine-resolution measurements of HDI do not exist globally for training their approach. Additionally, their approach uses proprietary data which we do not have access to (we have corresponded extensively with the authors in an effort to obtain access in order to respond to this comment). We can, however, compare the performance of our approach to Chi et al. predicting their Relative Wealth Index (RWI), which is identical to what we call “within-country IWI”. In general, our performance metrics are slightly higher than Chi et al., although direct comparison is complicated by differences in methods and data. We now add this to the discussion comparing to other prior approaches on lines 318 - 330:\nOur strategy is motivated by the limited resolution of available training data for HDI, but our results do not exhibit obvious compromises in performance relative to alternatives that exploit high-resolution labels. A related benchmark in this literature achieves ρ2=0.63-0.67 predicting a wealth index when training and evaluating at the DHS cluster resolution (16, 51). Though we train at the provincial level, not the DHS cluster level, our performance predicting DHS cluster IWI is competitive with this previous analysis ρ2=0.7; Table S1, col 1). Another benchmark in this literature achieves an R2 of 0.54 predicting RWI, which is conceptually identical to what we call within-country IWI, at the same DHS cluster level (17) (metric taken from a replication of their Figure 3B). Again, despite training at the provincial level rather than the DHS cluster level we achieve a within-country R2 of 0.56 predicting IWI at the cluster level. Direct comparison to both of these benchmarks, however, is complicated by differences in training and evaluation methodologies including our focus on explaining within-province variation and our corresponding mean-anchoring approach.\nWe also tried to additionally compare our performance predicting within-province, rather than within-country IWI, which is the preferred metric in our paper because we are interested in explaining fine-resolution variation in HDI within provinces that has yet to be previously estimated at global scale. Unfortunately, the replication data provided by Chi and co-authors do not allow us to calculate a within-province metric, and correspondence with their team indicates that they no longer have access to the data that would be necessary to do this.\n3.2. Ablation study: Excessive Contribution of Nightlight Data to the Full Model’s Performance\nAs described in the ridge regression, MOSAIKS and nightlight are the two primary features used for estimating HDI in a given region. Table S1-S3 showcase the model performance with ablations, where each component is excluded. However, upon reviewing the data in Table S1, it appears that the NL standalone model shows comparable performance to the full model in terms of ρ² and R². In some cases the NL model even overperforms the full model. For example, when predicted at municipality level in Mexico, within-country performance of MOSAIKS+NL presents 0.5 ρ² (0.45 R²) while that of NL is 0.58 ρ² (0.5 R²). In light of these results, the authors are encouraged to provide evidence supporting the meaningful contribution of MOSAIKS in the full model.\nThis is an interesting question and we thank the reviewer for raising it. It is clear throughout the multiple data sets and tests explored in our analysis that both MOSAIKS features and NL features individually contain useful signals and, in principle, the analysis could have been completed using either one and our qualitative findings would have nonetheless been obtained. However, through the process of our work, we have discovered that global performance for HDI using both data sets combined achieves the best results, and thus have proceeded with a focus on this combined model. Nonetheless, as the reviewer points out, the strength of the different signals from these two input data sets are expressed differently for different outcomes in different subsamples. Indeed, the inclusion of both data sets is valuable because it is unknown ex ante what information will be provided by each, and we find that each provides value in different contexts. The single result that the reviewer has isolated is an interesting and puzzling result that we are continuing to investigate in ongoing work; however, we do not yet have a complete explanation that we are satisfied with, and thus we plan to continue future work in this vein. We hope to present a more complete analysis that more fully evaluates how data from many satellite sensors (including others not used in this analysis) can be effectively and efficiently combined in SIML applications. However, this more complete treatment is well beyond the scope of this analysis, and it is not essential to the present work. Thus, throughout the manuscript we have simplified our presentation by focusing on the joint MOSAIKS + NL model that is our primary interest. However, to address the reviewer’s concern, we have now added additional discussion of this to our discussion of the “Value from combining daytime and nighttime imagery” in Supplementary Information Discussion S2. This section now reads:\nThe MOSAIKS-based approach can use image features from multiple sensors simultaneously when training models, a property that is used throughout this analysis to predict HDI from both daytime and nighttime imagery. Analyzing the performance of MOSAIKS models based on the type of satellite imagery used, we find that daytime and nighttime imagery together explain 7% more variation in provincial HDI deviations from the country mean than does nighttime imagery alone, improving model fit by 16% from R2 = 0.45 to 0.52 (Table S3). This improved performance from using daytime and nighttime imagery together is strongest in regions of low human development (HDI < 0.6) (Figure S7A), consistent with a previous finding that models using daytime imagery outperform models using nighttime imagery when predicting assets of the poorest populations in five African countries (20). Analyzing model performance for each component of HDI, we see that the improved performance predicting HDI using daytime and nighttime imagery stems from improved or comparable performance predicting each component of HDI (largest change in R2 is 0.12 for expected years of schooling, smallest is no change in R2 for life expectancy, Table S3).\nIn exploratory analysis of subsamples, we have observed that in several middle income countries with HDI between 0.7 and 0.8 (including those where we have municipal variation in HDI), within-country R-squared is sometimes higher when models are trained on nighttime imagery alone, relative to models that combine MOSAIKS and nighttime imagery. However, for other parts of the HDI distribution and on average, as described above, MOSAIKS features appear to add performance to the full model. We currently cannot explain why a nightlights-only model performs best for these particular countries when predicting HDI, and we do not know if this phenomena extends to non-HDI outcomes. In future work, we hope to present a more complete analysis that more fully evaluates how data from many satellite sensors, including others not used in this analysis, can be effectively and efficiently combined in SIML applications.\nIn addition to contributing to the full model performance on average, we also note that the MOSAIKS daytime imagery features on their own have substantial predictive performance, achieving an R2 of 0.42 predicting within-country provincial HDI variation and an R2 of 0.44 predicting within-province municipal variation in Indonesia, the country for which we have the HDI data most closely aligned with the date of our satellite imagery.\n4.1. Same weights β for linearization at tile, province, municipality levels.\nThe model assumes that the weights (β) representing the relationship between satellite imagery features and HDI are consistent across different spatial scales, such as tiles, provinces, and municipalities. However, this assumption—that the same β applies regardless of scale—does not appear to have been explicitly validated in this study. Given the differences in spatial aggregation and scale, it is critical to test whether this assumption holds, as it directly impacts the robustness and reliability of the model's estimates.\nWe thank the reviewer for suggesting this analysis, which is helpful for both validating the approach and understanding why it works. We have implemented the analysis suggested by the reviewer. However, we note that this test, as suggested by the reviewer and now implemented in our manuscript, is sufficient to demonstrate that model weights are transportable across scales of aggregation, but it is not necessary to pass this test in order for our main results to hold. Requiring that similar weights are independently recovered across multiple scales is not strictly necessary for one set of weights to be valid when applied to multiple aggregated scales of aggregation. Since our main analysis uses a large number of features relative to the number of training observations, weight selection during the ridge regression step could produce multiple practically-equivalent sets of weights when applied to different samples of data or different scales of aggregation. This is now also explained in the text when we present this test.\nWe now briefly mention the test in the main text on lines 82-83:\nSee Supplementary Information S5 for an empirical validation of the scale-invariance of model weights using this approach.\nWe discuss the test and its results in a supplementary discussion (lines 1202-1257):\nS5 Supplementary discussion assessing consistency of model weights across spatial scales\nA key feature of our approach is that it can be trained on and make predictions for units of arbitrary shape and size. We employ this approach to train on global provincial HDI data and make predictions of HDI for global municipalities and a 0.1˚ X 0.1˚ grid. For this approach to be effective, model weights estimated at the provincial level, must be able to make skillful predictions at the municipal and grid levels.\nOne way to understand how this approach works is to see that, in a linear model, the relationship between aggregated outcomes and aggregated features should be similar to the relationship between disaggregated outcomes and features. This is illustrated in Equations 2-3 of the main text. Rolf et al (12) provide additional mathematical explanation for relating predictions made using MOSAIKS features at image and sub-image scales. A primary goal of this manuscript is to propose that this approach can be used to address the challenge of limited training data in remote sensing applications by allowing for training on irregularly structured and sized observations -- which is not discussed in ref.(12) -- and to empirically test whether this works in practice. The primary evidence supporting this are the downscaling tests reported in Figure 2 and Table S1.\nHere, we additionally explore the question of why the approach works by empirically testing whether model weights estimated at aggregated and disaggregated scales are similar. To do so, we compare model weights between models of IWI trained at the provincial (N = 862) and DHS cluster (N = 51,996) scales. We use IWI for this experiment because there are a large number of aggregated and unaggregated observations that span the same spatial extent.\nA challenge in designing this experiment is that MOSAIKS features are correlated with each other, and there are a large number of features relative to the number of training observations. This means that the same information could load onto different features even when training and retraining at the same scale if we do not introduce additional constraints to the feature set. Put another way, different sets of model weights could give the same predictions and represent the same relationship between the imagery and outcome of interest. This is not an issue in our main application, since the set of weights obtained at an aggregated scale will remain valid if applied to a disaggregated scale, and vice versa. However, there is no guarantee that the same weights will be obtained if models are independently fit at both scales, since there are multiple valid ways to represent the data using the model features. Thus, for this experiment, we first transform our features into an orthogonal basis.\nWe use Principal Components Analysis (PCA) to project the MOSAIKS features into a feature space with independent (i.e., uncorrelated) features that contain the same information as the original features, following ref. (17). PCA can also be used to reduce the dimensionality of the feature space, which can aid interpretation in this setting by focusing on features that explain most of the variation in the imagery, and thus likely in the outcome of interest. We find that 100 PCA features explain > 99.9% of the variation in the original 4,000 MOSAIKS features in this context, and that a model trained using these 100 PCA features provides essentially identical predictions to a model trained using the 4000 original features (Figure S10A). This PCA model is thus practically identical to our MOSAIKS-based model but with independent features that represent an orthogonal basis. We use these orthogonalized and rotated MOSAIKS features to analyze whether model weights are consistent when training at different levels of aggregation.\nUsing these orthogonal MOSAIKS features, we find that model weights estimated using the (aggregated) provincial data are very similar to model weights that are independently estimated using (disaggregated) DHS cluster data (R2=0.75, Figure S10A). Note that when calculating R2 in this setting we weight by the fraction of variance in the MOSAIKS features each component explains, so that greater weight is placed on features that explain more variation in the MOSAIKS features, and likewise, in IWI. The high correspondence between weights estimated at aggregated and disaggregated scales indicates that the same satellite information is being used in the same way to predict IWI at both scales. This helps to explain how our approach is able to achieve skill in the downscaling applications illustrated in Figure 2 and Table S1.”\n4.2. Methodological novelty\nAnother methodological issue is the heavy reliance of this study's model on the MOSAIK framework, which was previously published in Nature Communications [1]. While it is noteworthy that this paper applies the approach to estimating different datasets (i.e., HDI) and provides the first global estimates at the second administrative level, it is difficult to identify significant methodological advancements compared to the earlier work. The primary novelty lies in the application context rather than in the development of the modeling approach itself, raising questions about the extent of its contribution beyond the adaptation to a new target variable.\nIf the methodological advancements are not substantial, it raises the question of whether the work would be better suited for publication as a Scientific Data paper rather than as a full research article. In such a case, the focus should be on rigorously validating the dataset to ensure its credibility and utility for future research and applications, rather than emphasizing methodological innovation.\n[1] Rolf, E. et al. (2021). A generalizable and accessible approach to machine learning with global satellite imagery. Nature Communications, 12(1), 1-11.\nWe respectfully but firmly disagree with the reviewer on this point. We believe that the manuscript makes substantial methodological advancements, and that the present analysis is out of scope for the journal Scientific Data.\nThe aim and scope of Scientific Data is “publishing descriptions of research datasets and articles on research data sharing”. This is a different objective than the contributions of the present analysis. For example, in one of our research lab’s prior publications in Scientific Data (Krasovich, 2022), we assemble, validate and document a data set of pre-existing water quality measurements from the Mississippi River Basin. This was in alignment with Scientific Data’s statement that its Data Descriptor Papers “describe open research datasets in a manner that promotes reuse, without reporting whether datasets support hypotheses or conclusions.” Scientific Data expressly prohibits the presentation of any material that goes beyond cataloging new data sets, stating: “Please note that Scientific Data does not publish traditional research articles using data to validate regular scientific hypotheses.” Thus, papers that are developing and exploring methods used to make new measurements are not generally published in Scientific Data.\nPapers, such as our present manuscript, that develop new techniques for measurement, implement large scale measurements (resulting in new data sets), and explore the implications of those new measurements are regularly published in general interest journals such as Nature Communications. For example, Hansen et al (“High-Resolution Global Maps of 21st-Century Forest Cover Change”, Science 2013); Kruitwagen (“A global inventory of photovoltaic solar energy generating units”, Nature, 2021); Chi et al (“Microestimates of wealth for all low- and middle-income countries”, PNAS, 2022); and Neugarten et al (“Mapping the planet’s critical areas for biodiversity and nature’s contributions to people”, Nature Communications, 2024). Similar to our analysis, these papers develop novel approaches to apply existing methods to a new context, construct valuable new global maps using these techniques, and describe new results that are obtained by inspecting and analyzing these new large-scale measurements.\nOur manuscript builds upon the MOSAIKS approach developed in Rolf et al., (2021) and the use of NL to measure economic activity developed in Henderson et al., (2012) to make several substantial methodological contributions. Primarily, it develops an approach that allows for training and predicting on irregularly shaped and sized polygons, which is generally not possible using existing SIML approaches (see lines 45-64 for details). This addresses a key limitation of the existing SIML literature -- the dearth of available training data -- by allowing models to be trained on coarse but plentiful administrative data. Using MOSAIKS in this way was not discussed in Rolf et al., (2021) which applied the approach to only square images of a constant size, following the existing literature.\nIn addition to proposing and developing this MOSAIKS/NL-based downscaling approach, the manuscript empirically demonstrates that the approach works well in practice (Figure 2), and provides evidence for why it works (Supplementary Information S5). This empirical demonstration of the developed approach is key for broad use of the approach and for trust in the created estimates of HDI.\nDeveloping this approach required a collection of specific methodological advances. For example, we found that to predict fine-scale local variation in the outcome of interest, SIML models should be trained on only fine-scale local variations, rather than the full variation across all the training data (lines 122-133). This combines a fixed-effect regression model specification, often used in econometrics, with a more traditional machine learning approach. The commonly used practice of training on the full variation in the outcome of interest -- both within and across countries -- we show, has substantially lower performance in our setting across all validation tests (Table S3). This led to the development of our “within-country” models, which we use to predict HDI. Another substantial development enabling our approach and its application to HDI was the production of a set of MOSAIKS features across nearly the entire global land surface. In contrast, Rolf et al. (2021), created MOSAIKS features and analysed less than 1% of the global land surface. This manuscript’s global dense featurization required roughly $60,000 of compute, and enabled us to produce HDI estimates across global municipalities, rather than for a small subset of the Earth’s surface. These features can be used, in combination with the developed approach, to downscale other variables of interest at large scale.\nReviewer #2 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.\nWe are grateful for your time and your support of early career researchers. Your collective comments have had a tremendous impact on the quality of this manuscript.\nReviewer #3 (Remarks to the Author):\nThe paper “Global high-resolution estimates of the United Nations Human Development Index using satellite imagery and machine learning” contains the first granular estimates of the UN’s Human Development Index. The paper develops a downscaling technique that uses provincial estimates to generate estimates at a more granular level. The paper is very well-written, to the point, and contains numerous relevant and convincing robustness checks. The authors anticipated and addressed many of my questions related to the interpretability of the model, its performance over time, its performance by HDI dimension, and whether the relationship between the features and the outcome is geographically stable. I have three comments, which I think could help improve the relevance and applicability of the model.\nWe thank the reviewer for their thoughtful and helpful comments. Please find our response to each below.\n1. Use of multiple imputation techniques.\nThe authors point out that the predictions have a much lower variance than the true distribution, which is also evident from several of the panels of Figure 2. If I am not mistaken, this means that the model systematically underpredicts the extent to which non-poor provinces have poor municipalities, as well as the extent to which poor provinces have non-poor municipalities. This seems to be an important issue given that perhaps the main purpose of the paper (as illustrated with the targeting example in Mexico) is to uncover such situations. Multiple imputation and small area estimation techniques have existed for decades to deal with the issue that the variance of the predicted values is too small. Could the authors use such techniques to recover more plausible predictions? I realize that small area estimation applications predict at the same level as which ground-truth data are available, so the authors are in a different situation here. Yet surely there are some assumptions about the error term one could make to recover more realistic predictions, perhaps utilizing the Mexican data where the true distribution of municipal estimates is available. If not attractive, and no attractive alternative exists, please explain why.\nWe appreciate the reviewer’s question and insights with respect to this.\nUnfortunately, we find that there is no clear way to expand the variance in predictions without reducing the accuracy of our predictions.\nPredicted values having lower variance than the true values is a common feature of predictive models and stems from the model not explaining all of the variance in the true values. For example, consider the linear model: HDI = βX + e. Under this model, Var(HDI) = Var(X + e), but Var(HDI) > Var(βX) so long as Var(e) is non-zero. Thus, any linear model for which the predictions (βX) do not explain all the variance in the outcome (i.e., R2 < 1) will have reduced variance of the predictions relative to the outcome. The more of the variance in the outcome the model can explain, the greater Var(βX) is relative to Var(e), and the less variance of the predictions will be deflated. Our model, which performs competitively to similar approaches in the literature despite training and evaluating on different scales (lines 318-323), explains roughly half of the within-country and within-province variation in HDI, so it makes sense that its predictions, like those of related models in the literature, have lower variance than the true values. The lower variance of the predictions means that, on average, the model will under-predict how poor relatively poor provinces within countries are and also under-predict how rich relatively rich provinces within countries are. And similarly for municipalities within provinces. While imperfect, these satellite-based predictions are still substantial improvements over the provincial values, which implicitly assume zero municipal variation within provinces.\nIt is not clear to us how existing multiple imputation and small area estimation techniques could be used to improve upon our current approach. Though multiple imputation can take many forms, it has two general elements that could potentially ameliorate issues related to deflated variance: re-scaling and adding variance.\nFollowing ref. (25), we could view the true municipal HDI values as missing, and impute them using the satellite-based HDI predictions calibrated to ground truth municipal HDI values from Indonesia, Mexico and Brazil. To evaluate this type of approach, we could train a calibration model for our estimates using data from Indonesia and Brazil (HDI = β𝐻𝐷𝐼 + e), and then use this calibration model to correct predicted HDI in Mexico (HDI_calibrated = β𝐻𝐷𝐼 + 𝑒). This linearly rescales the original HDI estimates to match the ground truth calibration values and adds an error term to better match the variance of predicted values to the true variance. We find that this approach reduces predictive performance in the Mexican data (Within-province R2 decreases from 0.29 to 0.03, ρ2 declines from 0.29 to 0.08) and, accordingly, reduces targeting performance (AUC=.86 to AUC=.79). Performance is reduced for two reasons. First, the calibration model learned on the Indonesian and Brazilian data is not a perfect fit for the Mexican data. Similar issues are likely to occur if calibrating on data from Mexico, Indonesia and Brazil and then correcting data from the rest of the world, which is arguably the most feasible application of this approach to the global setting. Second, adding an error term introduces additional noise into the estimates and is thus not preferable when trying to generate a single best estimate of the quantity of interest. While this added noise increases the variance of estimates, it also introduces error into the estimates, making them farther on average from the true values, which reduces targeting performance.\nWhile applying multiple imputation approaches to correct the HDI data is likely to be useful in some settings (25), we see that in this targeting setting it worsens performance. Thus, we maintain our estimates as they are, and allow users to implement multiple imputation using our open source code and freely available data if it would be of use in their particular setting. We note that there are many ways to potentially apply multiple imputation, but we see no reason that general features of rescaling, adding noise, or making multiple predictions of the target variable, are likely to improve our estimates in general.\nWith regards to small area estimation methods, we now explain how our approach is a type of small area estimation on lines 345-352:\nThis approach can be viewed as a type of regression-based technique for small area estimation using satellite imagery (53, 54). Though data limitations in this setting -- including the lack of fine-resolution global surveys of HDI -- preclude the direct implementation of most commonly used small area estimation techniques (e.g., (55), this approach follows the general small area estimation framework of combining limited measurements of the variable of interest (provincial HDI) with universally available axillary data informing the variable of interest (satellite imagery) to make accurate and precise fine-resolution predictions.\nWe view improving the model to more fully explain HDI as the best way to address this challenge of reduced variance. To this end, we try adding features from an additional satellite to the model. Unfortunately, this did not improve performance, indicating that there may be a limit to what can be predicted using satellite imagery in this setting. We discuss this on lines 331-344:\nHere, we use satellite imagery due to its rich information content, global availability, and near uniformity in quality across countries. To evaluate whether additional satellite data sources beyond visual daytime imagery and nighttime imagery might improve HDI estimates, we follow ref. (22) and add to the baseline model three additional index-based features constructed from Sentinel-2A satellite imagery that integrate knowledge of spectral properties of different ground conditions: the Normalized Difference Vegetation Index, Normalized Difference Water Index, and Normalized Difference Built-Up Index. We find that the model performance is essentially unchanged (Table S5), indicating that these additional features do not provide additional information beyond what is already captured by the MOSAIKS and NL features. While it is important to note that there is a limit to how well socioeconomic variables can be predicted using satellite imagery generally, and adding these additional features did not improve performance in this case, future work should nonetheless explore whether incorporating additional imagery sources and/or other ancillary data can improve these estimates (52).\n2. Discussion of advantages/disadvantages for targeting relative to alternative approaches\nThe policy relevance of the paper clearly comes from improved within-country targeting of resources, as cross-country targeting of resources tends to rely on country-level data. Yet it is unclear when countries armed with these estimates would use them for targeting resources. Countries with administrative data would probably use those for targeting, while countries with recent census and survey data would probably rely on small-area estimation techniques to generate granular measures of well-being (I realize small area estimation techniques rarely if ever have the HDI on the left-hand side, but they could have any multidimensional measure of well-being that can be recovered from surveys). What are the cases the authors envision the data generated could be applied? Perhaps in countries with no census, no survey data, no admin data? Or do you think this method works better than small-area estimation techniques? If so, what is the evidence to that end? This paper might be of interest for the discussion: https://doi.org/10.1016/j.jdeveco.2024.103352\nThank you for this question. We now provide a greater discussion of the potential use and value of these estimates for targeting on lines 297-308:\nThis application illustrates how fine-resolution HDI estimates can improve targeting of policies that would otherwise use coarser provincial measures, even though these fine-resolution estimates are imperfect. Using provincial measures implicitly assumes no within-provincial variation in HDI, so any positive ability to predict variation within provinces improves understanding of the spatial distribution of HDI. Users of these fine-resolution estimates should consider their specific policy context to determine whether these fine-resolution estimates, which explain 29% of the within-province HDI variation in Mexico, 20% in Brazil, and 53% in Indonesia, provide sufficient additional information to be useful in their setting. These estimates may be particularly valuable in data poor settings, where traditional data sources such as surveys are less available and reliable (15); only about half of the world’s poorest countries have conducted a census in the last decade (16, 26). These estimates may also be useful in cross-country settings where a consistent metric of welfare is desired.\nAnd we discuss how the approach in this manuscript relates to small area estimation approaches on lines 345-364:\nThis approach to producing HDI estimates can be viewed as a type of regression-based technique for small area estimation using satellite imagery (53, 54). Though data limitations in this setting -- including the lack of fine-resolution global surveys of HDI -- preclude the direct implementation of most commonly used small area estimation techniques (e.g., (55)), this approach follows the general small area estimation framework of combining limited measurements of the variable of interest (provincial HDI) with universally available axillary data informing the variable of interest (satellite imagery) to make accurate and precise fine-resolution predictions. A key difference between more traditional small area estimation techniques and ours is that we use a global-level auxiliary dataset that does not suffer from the challenge of construct validity across countries, although this comes with a tradeoff of needing to assume some degree of consistency between imagery and conditions on the ground. A recent comparison of poverty maps for Malawi produced using i) a small area estimation approach combining survey data and census data and ii) an alternative approach combining survey data and geospatial indicators including satellite imagery found that the two approaches produced very similar estimates, with a correlation exceeding 0.9 (56). This, paired with the performance of satellite imagery predicting HDI shown here, indicates that satellite imagery can be an effective substitute for census information when producing fine-resolution estimates of human wellbeing in settings where census data is not available. In locations where reliable census data is available, satellite imagery could serve as a complementary source of information.\n3. Interpretation of the model’s error\nThe authors conduct numerous different and relevant checks to test the performance of their model. The overarching challenge is that an ideal assessment of the model would require true granular HDI estimates which, except for in one circumstance, do not exist. The one genuine test of the error they can make suggests that the performance is moderate at best (Figure 2D), with an R^2 of 0.29, while the other one that comes close (2G) is likewise not too great. I think the authors ought to place greater emphasis on the point that the model fundamentally cannot be evaluated in a first-best manner and that second-best approximations suggest that one-third of the relevant variance can be predicted by the model.\nWe appreciate this thoughtful comment and agree that this is an important point to make clearly. In the text we write (lines 135-136):\nWe cannot directly evaluate the performance of municipality-level or grid-level HDI predictions worldwide because such highly-resolved estimates have not been previously constructed.\nAnd that (lines 149-153):\nNo test can directly validate the performance for downscaling HDI globally, since the data necessary for such a test do not exist; however, all three of these large-scale tests taken together document the effectiveness of our downscaling strategy in general -- using global socioeconomic data similar to HDI -- and for HDI in particular -- using municipal HDI data for three countries.\nWe also now add that (lines 211-212):\nComparisons to municipal data on HDI, IWI, and NL indicate that models trained on provincial data can explain 20-57% of within-province municipal variation.\nWe have also added two additional direct evaluations of our municipal HDI predictions using data from Indonesia and Brazil. We discuss model performance comparing our predictions to these estimates on lines 159-177 and visualize performance in Figure 2.\nDownscaling HDI in Mexico, Brazil and Indonesia\nAs a direct evaluation of HDI downscaling performance, we compare municipal HDI predictions from the satellite-based model trained on provincial HDI deviations from the country mean to municipal HDI derived from census-based calculations in Mexico (9), Brazil (35), and Indonesia (34) (Methods 2.3). In Mexico, downscaled HDI predictions explain 45% of the municipal HDI variation overall (Figure 2C) and 29% of the within-province variation (Figure 2D). In Brazil, HDI predictions explain 48% of municipal HDI variation overall, and 20% of the within-province variation. And in Indonesia, HDI predictions explain 61% of the municipal HDI variation overall and 53% of the within-province variation. It is encouraging that HDI predictions align better with census-based measures for Indonesia than for Mexico or Brazil because measures for Indonesia are from 2019, which aligns with our satellite-based predictions of within-province HDI variation, while measures for Mexico and Brazil are from 2010. These older HDI measures could differ from our satellite-based predictions in part due to changes in HDI since the measurements were taken. Additionally, some portion of the misalignment between satellite-based predictions and survey estimates likely arises as a result of errors in the survey data itself, a widely recognized issue (15) that we are unable to assess. Together, these results indicate that our method for SIML-based downscaling improves our understanding of the spatial distribution of HDI in these three example countries; although, it is not a complete substitute for survey-based estimates when such data are available.\nThe updated Figure 2 is reproduced below:\nAnd the updated associated Table S1 is reproduced as well, with some modifications to accommodate the additional analysis:\nThe new data are described in the methods on lines 493-518:\nMunicipality-level HDI\nWe compare our municipal HDI estimates with census-derived municipal estimates for HDI, where these data exist.\nIndonesia Time series estimates of HDI at the municipality level are made publicly available by Badan Pusat Statistik (BPS), the statistics agency of Indonesia (63). We use estimates from 2019, which makes these, to our knowledge, the only available municipal HDI data that come from the same year as our satellite imagery.\nBrazil The Human Development Report Office office of the United Nations Development Programme has derived HDI data at the municipality level for Brazil, using census data (35). The most recent year these data are available is 2010, which we use in this analysis. The census-derived data have a different mean than the 2019 HDI data that we use elsewhere in this analysis; though, this has no influence on the within-country or within-province evaluation metrics (Figure 2 C,D) because predictions and observations are demeaned at the country and province level, respectively, before the metrics are calculated.\nMexico Census derived estimates of HDI are also available in Mexico for the year 2010, constructed by ref. (9). As with Brazil, these data have a different mean than the 2019 HDI data; though, again, that has no influence on the within-country or within-province evaluation metrics.\nWhen certain components of HDI are not directly available at the municipal level, producers of these datasets use close proxies. For example the BPS calculates municipal HDI data in Indonesia using data on real expenditure rather than GNIpc (34). And when calculating municipal HDI in Mexico, ref. (9) use the child survival rate rather than life expectancy at birth for the health index and an asset index rather than GNIpc for the standard of living index. Likewise, provincial HDI estimates are also constructed using proxies when direct measurements of HDI components are not available (7). Discrepancies in how HDI is calculated at the municipal and provincial levels may contribute to differences between our satellite-based HDI estimates and these survey-based HDI estimates.\nThese direct validations of the downscaling approach using observations of subnational HDI from Mexico, and now Indonesia and Brazil as well, supplement the additional downscaling tests applying the method to nighttime lights and the IWI. In all tests, the approach is able to predict substantial variation in municipal HDI, or related wealth indices, within the provincial units on which the model was trained. This, in combination with the rest of the paper’s analyses, provides substantial evidence that the downscaling approach provides new and useful information on HDI at fine resolution globally.\nWe do acknowledge, however, that these estimates are far from perfect and that “there is a limit to how well socioeconomic variables can be predicted using satellite imagery generally” (lines 340-341). We now provide additional discussion of the potential utility of these imperfect estimates on lines 297-308:\nThis application illustrates how fine-resolution HDI estimates can improve targeting of policies that would otherwise use coarser provincial measures, even though these fine-resolution estimates are imperfect. Using provincial measures implicitly assumes no within-provincial variation in HDI, so any positive ability to predict variation within provinces improves understanding of the spatial distribution of HDI. Users of these fine-resolution estimates should consider their specific policy context to determine whether these fine-resolution estimates, which explain 29% of the within-province HDI variation in Mexico, 20% in Brazil, and 53% in Indonesia, provide sufficient additional information to be useful in their setting. These estimates may be particularly valuable in data poor settings, where traditional data sources such as surveys are less available and reliable (15); only about half of the world’s poorest countries have conducted a census in the last decade (16, 26). These estimates may also be useful in cross-country settings where a consistent metric of welfare is desired.\nWe also note that our model estimates, while imperfect, perform competitively with prior approaches in the literature despite training on coarse provincial data (see the discussion on lines 318-330 for details).\nReviewer #4 (Remarks to the Author):\nSummary\nThe manuscript by Sherman et al. presents a novel method to downscale the United Nations Human Development Index (HDI) using a combination of high-resolution daytime and nighttime satellite imagery and machine learning. The study addresses the critical issue of aggregation bias in traditional HDI measurements by demonstrating that a significant fraction of the global population is misclassified when relying solely on country- or province-level data. Validation using survey-based estimates in Mexico and comparisons with alternative socioeconomic indicators (e.g., the International Wealth Index and nighttime lights) support the robustness of the proposed approach. Overall, the work offers a promising avenue to support more spatially precise policymaking and contributes substantially to the literature on satellite-based socioeconomic measurements.\nWe thank the reviewer for their thoughtful and constructive comments. Please find our response to each below.\nMajor Comments\n1. Introduction:\nThe paper assumes how HDI is constructed at the national and municipal levels, but it would be beneficial to explicitly mention the range of HDI (0 to 1), its variation across countries, and the weights assigned to each component (education, health, and income).\nWe add this information on lines 468-479:\nThe United Nations Human Development Index is a composite measure used to assess a country's average achievements in three key dimensions of human development: health, education, and standard of living (4). Health is measured by life expectancy at birth; education is evaluated using a combination of mean years of schooling for adults and expected years of schooling for children; and standard of living is assessed through gross national income (GNI) per capita, adjusted for purchasing power parity (PPP). The HDI applies a logarithmic transformation to GNI to account for the diminishing benefits of increased income. Each of these components is normalized on a scale from 0 to 1, and the HDI is calculated as the geometric mean of the three dimension indices, giving equal weight to each dimension. This method allows the HDI to reflect not just economic wealth, but also broader aspects of well-being. In 2019, the average HDI across countries was 0.72, with a standard deviation of 0.15, a minimum of 0.36 in Somalia and a maximum of 0.96 in Switzerland. (Figure 3A).\nIn Mexico, municipal-level HDI estimation relies on the population census for education and health, but the income variable is estimated using small area estimation techniques (Elbers, Lanjouw, and Lanjouw 2003). These estimations are inherently uncertain. It would strengthen the paper to contrast the proposed method with these techniques, highlighting not only the limitations of census data for small areas but also the challenges in obtaining statistically valid income estimates at the municipal level.\nWe now discuss the uncertainty in the Mexican municipal HDI estimates on lines 510-518:\nWhen certain components of HDI are not directly available at the municipal level, producers of these datasets use close proxies. For example the BPS calculates municipal HDI data in Indonesia using data on real expenditure rather than GNIpc (34). And when calculating municipal HDI in Mexico, ref. (9) use the child survival rate rather than life expectancy at birth for the health index and an asset index rather than GNIpc for the standard of living index. Likewise, provincial HDI estimates are also constructed using proxies when direct measurements of HDI components are not available (7). Discrepancies in how HDI is calculated at the municipal and provincial levels may contribute to differences between our satellite-based HDI estimates and these survey-based HDI estimates.\nWe also now discuss how our approach fits within the range of small area estimation techniques on lines 345-364:\nThis approach to producing HDI estimates can be viewed as a type of regression-based technique for small area estimation using satellite imagery (53, 54). Though data limitations in this setting -- including the lack of fine-resolution global surveys of HDI -- preclude the direct implementation of most commonly used small area estimation techniques (e.g., (55)), this approach follows the general small area estimation framework of combining limited measurements of the variable of interest (provincial HDI) with universally available axillary data informing the variable of interest (satellite imagery) to make accurate and precise fine-resolution predictions. A key difference between more traditional small area estimation techniques and ours is that we use a global-level auxiliary dataset that does not suffer from the challenge of construct validity across countries, although this comes with a tradeoff of needing to assume some degree of consistency between imagery and conditions on the ground. A recent comparison of poverty maps for Malawi produced using i) a small area estimation approach combining survey data and census data and ii) an alternative approach combining survey data and geospatial indicators including satellite imagery found that the two approaches produced very similar estimates, with a correlation exceeding 0.9 (56). This, paired with the performance of satellite imagery predicting HDI shown here, indicates that satellite imagery can be an effective substitute for census information when producing fine-resolution estimates of human wellbeing in settings where census data is not available. In locations where reliable census data is available, satellite imagery could serve as a complementary source of information.\n2. Methodological Clarity:\nWhile the authors discuss the MOSAIKS method, a clearer explanation with a more accessible example would enhance understanding. Figure 1 provides a visual representation, but the role of colors and the integration of socioeconomic variables could be explained more explicitly. A simplified schematic or a step-by-step breakdown of Figure 1 would aid readers unfamiliar with MOSAIKS in grasping how the method links coarse provincial data with fine-resolution predictions.\nWe thank the reviewer for this helpful comment. To improve clarity of the methods we have expanded the schematic of our methods and their description to include a discussion not only of how the features capture information from the color and texture of the imagery, but how this information about color and texture is used to predict HDI. The updated Figure S1 is reproduced below and also now referenced in the caption to Figure 1.\nThe paper could delve deeper into the comparison between the proposed method and small area estimates (SAE). It would be valuable to discuss whether the ML-based downscaling approach offers advantages over SAE, particularly in terms of variance and accuracy.\nAs mentioned in the response to a previous comment, we now discuss how our approach fits within the range of small area estimation techniques on lines 345-364:\nThis approach to producing HDI estimates can be viewed as a type of regression-based technique for small area estimation using satellite imagery (53, 54). Though data limitations in this setting -- including the lack of fine-resolution global surveys of HDI -- preclude the direct implementation of most commonly used small area estimation techniques (e.g., (55)), this approach follows the general small area estimation framework of combining limited measurements of the variable of interest (provincial HDI) with universally available axillary data informing the variable of interest (satellite imagery) to make accurate and precise fine-resolution predictions. A key difference between more traditional small area estimation techniques and ours is that we use a global-level auxiliary dataset that does not suffer from the challenge of construct validity across countries, although this comes with a tradeoff of needing to assume some degree of consistency between imagery and conditions on the ground. A recent comparison of poverty maps for Malawi produced using i) a small area estimation approach combining survey data and census data and ii) an alternative approach combining survey data and geospatial indicators including satellite imagery found that the two approaches produced very similar estimates, with a correlation exceeding 0.9 (56). This, paired with the performance of satellite imagery predicting HDI shown here, indicates that satellite imagery can be an effective substitute for census information when producing fine-resolution estimates of human wellbeing in settings where census data is not available. In locations where reliable census data is available, satellite imagery could serve as a complementary source of information.\nWe also expand our comparison with other related approaches in the literature that seek to estimate measures of human wellbeing at fine resolution on lines 318-330:\nOur strategy is motivated by the limited resolution of available training data for HDI, but our results do not exhibit obvious compromises in performance relative to alternatives that exploit high-resolution labels. A related benchmark in this literature achieves ρ2=0.63-0.67 predicting a wealth index when training and evaluating at the DHS cluster resolution (16, 51). Though we train at the provincial level, not the DHS cluster level, our performance predicting DHS cluster IWI is competitive with this previous analysis ρ2=0.7; Table S1, col 1). Another benchmark in this literature achieves an R2 of 0.54 predicting RWI, which is conceptually identical to what we call within-country IWI, at the same DHS cluster level (17) (metric taken from a replication of their Figure 3B). Again, despite training at the provincial level rather than the DHS cluster level we achieve a within-country R2 of 0.56 predicting IWI at the cluster level. Direct comparison to both of these benchmarks, however, is complicated by differences in training and evaluation methodologies including our focus on explaining within-province variation and our corresponding mean-anchoring approach.\nThe paper does not expand on the consistency of estimates in well-being over time. Specifically, it would be insightful to investigate instances where the official HDI shows an increase, while alternative measures like SIML suggest a decrease (or viceversa). Are there such cases?\nThank you for this comment. We focus this manuscript on estimating fine-resolution spatial variation in HDI. We do so because existing provincial measures do not resolve within-province differences in human wellbeing, and because spatial variation in HDI is generally 60 times larger than temporal variation. As described in Methods Section 4.5, we construct fine-resolution global estimates of HDI from 2012-2021 by adding time-constant satellite-based estimates of municipal HDI deviations from the provincial mean onto time-varying survey-based provincial values over this temporal range. Thus, we do not specifically predict or evaluate changes in the within-province distribution of HDI over time. All temporal changes in our estimates stem from temporal changes in the provincial values that the municipal estimates are anchored to. Supplementary Information Section S3 provides further discussion of and analysis on this topic.\nTo clarify this for readers we have updated our discussion of this topic in the conclusion to read:\nWe have produced global downscaled estimates of HDI for 2012-2021 by combining existing provincial measures with fine-resolution satellite estimates. This approach estimates municipal HDI in each year by adding satellite-based estimates of municipal HDI deviations from the provincial mean, which are time-constant, onto time-varying provincial values calculated from surveys (7). These municipal values are appropriate for applications comparing levels of HDI across locations within a specific moment in time. They cannot be used to evaluate changes in the distribution of HDI within-provinces over time. Current data does not allow us to distinguish performance between our validated approach and an approach that estimates local trends in HDI (Figure S8 and Supplementary Information S3). Developing additional approaches for tracking and validating subnational trends in HDI is an important area for future research.\nReviewer #4 (Remarks on code availability):\nThe link works and seems to be very informative:\ngithub.com/Global-Policy-Lab/hdi_downscaling_mosaiks\nI did not install the files, but it seems that everything is reproducible.\nThank you for reviewing our code and data. We are committed to ensuring that all data are available and that all analyses are replicable."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I appreciate the authors’ efforts and the potential value of high-resolution HDI-related data. I have carefully evaluated the authors’ rebuttal and revised materials in light of my initial review. While I appreciate the authors’ efforts, the key concerns remain insufficiently addressed. In my judgment, addressing these issues would require substantial new work and re- framing that goes beyond a reasonable revision and would effectively constitute a new study.\n\nHere are three issues that I am not still convinced by the manuscript and authors' responses.\n\n1. Low model performance\nModel performance at the target spatial scales is too low to support the main claims and intended uses. The manuscript validates municipality-level predictions using province-level HDI data from three countries (Indonesia, Brazil, Mexico). The authors focus on “explaining within-province variation” (manuscript, line 330), and this is the “preferred metric in (their) paper because (they) are interested in explaining fine-resolution variation in HDI within provinces that has yet to be previously estimated at global scale” (response, pp. 15-16).\nHowever, the reported within-province predictive performance averages about R^2 ≈ 0.34 (Brazil 0.20, Mexico 0.29, Indonesia 0.53). This is substantially below what is commonly seen and expected in the satellite-based socioeconomic prediction literature for policy-relevant applications (typically R^2 ≥ 0.5). Given this level of performance and the scale mismatch in validation, the headline claims—particularly regarding widespread misclassification of HDI quintiles and improved decision-making—are not sufficiently substantiated.\nIn addition, a simple, available baseline outperforms the authors’ approach in at least one country. In my first-round review, I requested a within-province baseline using Meta’s Relative Wealth Index (RWI) for Mexico (Chi et al., 2022). The authors responded that it was not possible “to calculate a within-province metric” (response, p. 16). Alternatively, I simply computed the within-province relationship between municipal MHDI and the mean RWI by municipality in Mexico (N = 2,456; excluding Bacalar due to missing MHDI). MHDI data was accessed through the website of authors. This baseline achieved R^2 = 0.364 at the municipality level, exceeding the authors’ reported value for Mexico (R2 = 0.29). This indicates that a simple, readily available baseline can match or outperform the proposed approach on the stated task.\n\n2. Lack of Validation for time-series estimates\nDuring the first round of review, I asked the authors to provide proper validation of time-series estimates on HDI. However, the authors stated that “we use the satellite imagery to downscale annual first level administrative HDI estimates to higher spatial resolution, but do not predict or evaluate changes in the within-province distribution of HDI over time. (Response, p. 11)” and “This approach assumes that the spatial pattern of HDI within provinces does not change over time; relaxing this assumption gives similar results (Supplementary Information S3).“\nNevertheless, the manuscript proposes to release annual maps for 2012–2021. In practice, when this manuscript is published in Nature Communications, there are high possibilities for some readers to use these data for time-series comparisons and policy evaluation despite the authors’ guideline in the manuscript. Without any temporal validation (e.g., consistency across years, sensitivity to shocks, stability of rankings, calibration of year-to-year changes), this might create a substantial risk of misuse and misinterpretation. Given that the study’s primary objective is to characterize fine-scale spatial variation in HDI, what is the rationale for releasing annual maps for 2012–2021?\n\n3. Methodological novelty\nI raised the heavy reliance of this study’s model on the MOSAIK framework, which was previously published in Nature Communications (Rolf et al., 2021). However, the authors disagree with my concern with several methodological contributions they assert. The authors argue novelty in training and predicting on irregularly shaped and sized polygons to leverage coarse administrative labels. “Training and predicting on irregularly shaped and sized polygons, which is generally not possible using existing SIML approaches. This addresses a key limitation of the existing SIML literature -- the dearth of available training data -- by allowing models to be trained on coarse but plentiful administrative data. (response p. 22)”. Unfortunately, the similar ideas have been already proposed such as Han et al. (2020).\nOther touted advances—training on fine-scale local variation, using a fixed-effects specification, and expanding MOSAIKS features from ~1% to near-global coverage (response p. 22)—appear to be incremental refinements and engineering scale-up rather than a substantive methodological contribution. The manuscript’s empirical demonstrations do not, in my view, establish a new methodological paradigm beyond what has been introduced in the literature.\nReferences\nChi et al. (2022). Microestimates of wealth for all low-and middle-income countries. Proceedings of the National Academy of Sciences 119, e2113658119\nHan, S. et al. (2020). Lightweight and Robust Representation of Economic Scales from Satellite Imagery. Proceedings of the AAAI Conference on Artificial Intelligence, 34(01), 428-436. https://doi.org/10.1609/aaai.v34i01.5379\nRolf, E. et al. (2021). A generalizable and accessible approach to machine learning with global satellite imagery. Nature Communications, 12(1), 1-11.", "reviewer_3": "Thank you to the authors for replying to my last set of questions. I have just two follow-up questions which I think can be handled relatively easily.\n\n1. I am still struggling a bit with the fact that the ranking of predicted values within a country will be biased against poor municipalities in non-poor regions and vice versa. If I am not mistaken, this systematic bias would not arise if the predictions were made in levels instead of deviations from mean values. I understand such predictions would perform worse in terms of R^2, but perhaps the exclusion/inclusion errors for targeting would be better? It should be easy for the authors to reject this hypothesis with their Mexican, Brazilian, and Indonesian data. If the AUC indeed is worse under this approach, I don’t think any further changes are needed to the manuscript on this topic.\n\n2. Thanks to the authors for clarifying when the proposed data can be useful for targeting. I agree that the application illustrates how fine-resolution HDI estimates can improve targeting of policies that would otherwise use coarser provincial measures. Yet I am still unaware of any cases where coarser HDI estimates were used for targeting. It would be helpful if the authors could cite a handful of such cases to document that this is tackling a widespread policy issue. Even if such cases do not exist, I think the fine-resolution HDI estimates have tremendous value, but perhaps more in terms of providing vital data for the research community and increasing our understanding of human wellbeing globally, but less for targeting purposes."}, "author_response": "We thank the reviewer for their time, thorough engagement, and valuable feedback and suggestions.\nBased on these comments, we have added a paragraph to the Discussion that explicitly discusses these HDI data from a policymakers perspective and acknowledges that policymakers face tradeoffs in electing to use new sources of data.\n“Policymakers will face a number of complex considerations before using these data in practice. Broadly, policymakers can benefit from algorithmically-informed decisions that are transparent and explainable (56) and there may be costs to using data for decision-making that is fundamentally harder to interpret and explain than alternative decisions made using traditional survey data. In addition, policymakers will have to decide whether and how it is appropriate to use a global dataset that we have only been able to directly validate in three countries. Third, policymakers may benefit from technical evaluations that interpret the performance here so that they can assess the marginal benefits of using these data for their specific use-case, recognizing that reasonable people may disagree about whether the data provided here achieve high enough performance to merit its use for specific applications. Future work should investigate improvements in remote sensing model interpretability that can support transparent policy-making and aid in understanding potential sources of systematic bias (55,57,58).”\nWe have also added more strength to our statement about the continuing need for survey data in Results Section 2.\n“We emphasize that these data are not a complete substitute for survey-based estimates and that our model could not be trained or evaluated without ground-truth surveys.”"}]

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