gremlin97/RemoteSensingCorpus · Datasets at Hugging Face

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Accepted as a paper at ICLR 2023 Workshop on Machine Learning for Remote Sensing
3 S TRUCTURES AND PATTERNS IN SPATIAL AND REMOTELY SENSED DATA
Geospatial and remotely sensed data exhibit distinct structures. For example, the chosen extent and
scale of a spatial prediction unit ( ℓin §2) has important implications for the design, use, and evalua-
tion of geospatial ML models, evidenced by the phenomena of “modiﬁable areal unit problem” and
“ecological fallacy” (Haining, 2009; Nikparvar & Thill, 2021; Yuan & McKee, 2022). Here, I focus
on two key factors of geospatial data that affect the validity of geospatial ML evaluation methods.
3.1 S PATIAL STRUCTURES : (A UTO)CORRELATION AND COVARIATE SHIFT
One key phenomena exhibited by many geopsatial data is that values of a variable (e.g. tree canopy
height) are often correlated across locations. Formally, for random process Z, thespatial autocor-
relation function is deﬁned as RZZ(ℓi,ℓj) =E[Z(ℓi)Z(ℓj)]/σiσj, whereσi,σjare the standard
deviations associated with Z(ℓi),Z(ℓj). For geospatial variables, we might expect RZZ(ℓi,ℓj)>0
whenℓiandℓjare closer together, namely that values of Zat nearby points tend to be closer in
value. The degree of spatial autocorrelation in data can be assessed with statistics such as Moran’s
Iand Geary’s C, and semi-variogram analsyes (see, e.g. (Gaetan & Guyon, 2010)).
Spatial autocorrelations and correlations between predictor and label variables can be an important
source of structure to leverage in geospatial ML models (Rolf et al., 2020; Klemmer & Neill, 2021),
yet they also present challenges. Models can “over-rely” on spatial correlations in the data, leading
to over-estimated accuracy despite poor spatial generalization performance. Overﬁtting to spatial
relationships in training data is of particular concern in the when data distributions differ between
training regions and regions of use. Such covariate shifts are common in geospatial data, e.g. across
climate zones, or spectral shifts in satellite imagery (Tuia et al., 2016; Hofﬁmann et al., 2021).
Presence of spatial correlations or domain shift alone do not invalidate assessing map accuracy with
a probability sample (§2.1). However, when evaluation is limited to existing data, issues of data
availability and representivity can amplify the challenges of geospatial model evaluation.
3.2 A VAILABILITY ,QUALITY ,AND REPRESENTIVITY OF GEOSPATIAL EVALUATION DATA
Many geospatial datasets exhibit gaps in coverage or quality of data. Meyer & Pebesma (2022) evi-
dence trends of geographic clustering around research sites primarily in a small number of countries,
across three datasets used for global mapping in ecology. Oliver et al. (2021) ﬁnd geographical bias
in coverage of species distribution data aggregated from ﬁeld observation, sensors measurements,
and citizen science efforts. Burke et al. (2021) note that the frequency at which nationally represen-
tative data on agriculture, population, and economic factors are collected varies widely across the
globe. While earth observation data such as satellite imagery have comparatively much higher cov-
erage across time and space (Burke et al., 2021), coverage of commercial products has been shown
to be biased toward regions of high commercial value (Dowman & Reuter, 2017).
Filling in data gaps is goal for which geospatial ML can be transformative (§2.2), yet these same
gaps complicate model evaluation. When training data are clustered in small regions, this can affect
our ability to train a high-performing model. When evaluation data are clustered in small regions,
this affects our ability to evaluate geospatial ML model performance at all.
4 S PATIALLY -AWARE EVALUATION METHODS : A BRIEF OVERVIEW
In §3, we established that geospatial data generally exhibit spatial correlations and data gaps, even
when target use areas Dare small. It is well documented that calculating accuracy indices with
non-spatial validation methods (e.g. standard k-fold cross-validation) will generally over-estimate
performance in such settings. Spatially-aware evaluation methods can control the spatial distribution
of training and validation set points to better simulate conditions of intended model use.
4.1 S PATIAL CROSS -VALIDATION METHODS
Several spatial cross-validation methods have been proposed that reduce spatial dependencies be-
tween train set points ℓ∈S trainfrom evaluation set points ℓ∈S eval. Spatial cross-validation methods
3
Accepted as a paper at ICLR 2023 Workshop on Machine Learning for Remote Sensing
typically stratify training and evaluation instances by larger geographies (Roberts et al., 2017; Valavi
et al., 2018) e.g. existing boundaries, spatial blocks, or automatically generated clusters. Buffered
cross-validation methods (such as spatial leave-one-out (Le Rest et al., 2014), leave-pair out (Airola
et al., 2019) and k-fold cross validation (Pohjankukka et al., 2017)) control the minimum distance
from any training point to any evaluation point. In addition to evaluating model performance, spa-
tial cross-validation has also been suggested as a way to to improve model selection and parameter
estimation in geospatial ML (Meyer et al., 2019; Schratz et al., 2019; Roberts et al., 2017).
While separating ℓ∈S trainfromℓ∈S evalcan reduce the amount of correlation between training and
evaluation data, a spatial split also induces a higher degree of spatial extrapolation to the learning
setup and potentially reduces variation in the evaluation set labels. As a result, it is possible for
spatial validation methods to systematically under-report performance, especially in interpolation
regimes (Roberts et al., 2017; Wadoux et al., 2021). In a different ﬂavor from the evaluation methods
above, Mil `a et al. (2022) propose to match the distribution of nearest neighbor distances between
train and evaluation set points to the corresponding distances between train set and target use area.
4.2 O THER SPATIALLY -AWARE VALIDATION EVALUATION METHODS
When the intended use of a geospatial model is to generate predictions outside the training distribu-
tion, it is critical to test the model’s ability to generalize across different conditions. For example,
studies have varied the amount of spatial extrapolation required by changing parameters of the spa-
tial validation setups in §4.1 , e.g. with buffered leave one out (Ploton et al., 2020; Brenning, 2022)
and checkerboard designs (Roberts et al., 2017; Rolf et al., 2021). Jean et al. (2016) assess extrapola-
tion ability across pairs of countries by iteratitvely training in one region and evaluating performance
in another. Rolf et al. (2021) ﬁnd that the distances at which a geospatial model has extrapolation
power can differ substantially depending on the properties of the prediction variable.
It is always critical to put the reported performance of geospatial ML models in context. Visualizing
the spatial distributions of predictions and error residuals can help expose overreliance on spatially
correlated predictors (Meyer et al., 2019) and sub-regions with low local model performance. Com-
paring performance to that of a baseline model built entirely on spatial predictors can contextualize
the value-add of a new geospatial model (Fourcade et al., 2018; Rolf et al., 2021).
5 T AKING STOCK : CONSIDERATIONS AND OPPORTUNITIES
Comprehensive reporting of performance is critical for geospatial ML methods, especially as stated
gains in research progress make their way to maps and decisions of real-world consequence. Eval-
uating performance of geospatial models is especially challenging in the face of spatial correlations
and limited availability or representivity of data. This means non-spatial data splits are generally
unsuitable for geospatial model evaluation with most existing datasets. Spatially-aware validation
methods are an important indicator of model performance including spatial generalization; however,
they generally do not provide valid statistical estimates of prediction map accuracy. This brings us
to end with three key opportunities for improving the landscape of geospatial ML evaluation:
Opportunity 1: Invest in evaluation data to measure map accuracy and overall performance of
geospatial models. When remote annotations are appropriate, labeling tools (e.g. Robinson et al.
(2022)) can facilitate the creation of probability-sampled evaluation datasets. Data collection and
aggregation efforts can focus on ﬁlling existing geospatial data gaps (Paliyam et al., 2021) or simu-
lating real-world prediction conditions like covariate or domain shift (Koh et al., 2021).
Opportunity 2: Invest in evaluation frameworks to precisely and transparently and report perfor-
mance and valid uses of a geospatial ML model ( `a la “model cards” (Mitchell et al., 2019)). This
includes improving spatial baselines, expanding methods for reporting uncertainty over space, and
delineating “areas of applicability” for geospatial models, e.g. as in Meyer & Pebesma (2022).
Opportunity 3: If the available data and evaluation frameworks are insufﬁcient, explain the limita-
tions of what types of performance can be evaluated . Distinguish between performance measures
that estimate a statistical parameter and those that indicate potential skill for a possible use case.

2

Accepted as a paper at ICLR 2023 Workshop on Machine Learning for Remote Sensing

3 S TRUCTURES AND PATTERNS IN SPATIAL AND REMOTELY SENSED DATA

Geospatial and remotely sensed data exhibit distinct structures. For example, the chosen extent and

scale of a spatial prediction unit ( ℓin §2) has important implications for the design, use, and evalua-

tion of geospatial ML models, evidenced by the phenomena of “modiﬁable areal unit problem” and

“ecological fallacy” (Haining, 2009; Nikparvar & Thill, 2021; Yuan & McKee, 2022). Here, I focus

on two key factors of geospatial data that affect the validity of geospatial ML evaluation methods.

3.1 S PATIAL STRUCTURES : (A UTO)CORRELATION AND COVARIATE SHIFT

One key phenomena exhibited by many geopsatial data is that values of a variable (e.g. tree canopy

height) are often correlated across locations. Formally, for random process Z, thespatial autocor-

relation function is deﬁned as RZZ(ℓi,ℓj) =E[Z(ℓi)Z(ℓj)]/σiσj, whereσi,σjare the standard

deviations associated with Z(ℓi),Z(ℓj). For geospatial variables, we might expect RZZ(ℓi,ℓj)>0

whenℓiandℓjare closer together, namely that values of Zat nearby points tend to be closer in

value. The degree of spatial autocorrelation in data can be assessed with statistics such as Moran’s

Iand Geary’s C, and semi-variogram analsyes (see, e.g. (Gaetan & Guyon, 2010)).

Spatial autocorrelations and correlations between predictor and label variables can be an important

source of structure to leverage in geospatial ML models (Rolf et al., 2020; Klemmer & Neill, 2021),

yet they also present challenges. Models can “over-rely” on spatial correlations in the data, leading

to over-estimated accuracy despite poor spatial generalization performance. Overﬁtting to spatial

relationships in training data is of particular concern in the when data distributions differ between

training regions and regions of use. Such covariate shifts are common in geospatial data, e.g. across

climate zones, or spectral shifts in satellite imagery (Tuia et al., 2016; Hofﬁmann et al., 2021).

Presence of spatial correlations or domain shift alone do not invalidate assessing map accuracy with

a probability sample (§2.1). However, when evaluation is limited to existing data, issues of data

availability and representivity can amplify the challenges of geospatial model evaluation.

3.2 A VAILABILITY ,QUALITY ,AND REPRESENTIVITY OF GEOSPATIAL EVALUATION DATA

Many geospatial datasets exhibit gaps in coverage or quality of data. Meyer & Pebesma (2022) evi-

dence trends of geographic clustering around research sites primarily in a small number of countries,

across three datasets used for global mapping in ecology. Oliver et al. (2021) ﬁnd geographical bias

in coverage of species distribution data aggregated from ﬁeld observation, sensors measurements,

and citizen science efforts. Burke et al. (2021) note that the frequency at which nationally represen-

tative data on agriculture, population, and economic factors are collected varies widely across the

globe. While earth observation data such as satellite imagery have comparatively much higher cov-

erage across time and space (Burke et al., 2021), coverage of commercial products has been shown

to be biased toward regions of high commercial value (Dowman & Reuter, 2017).

Filling in data gaps is goal for which geospatial ML can be transformative (§2.2), yet these same

gaps complicate model evaluation. When training data are clustered in small regions, this can affect

our ability to train a high-performing model. When evaluation data are clustered in small regions,

this affects our ability to evaluate geospatial ML model performance at all.

4 S PATIALLY -AWARE EVALUATION METHODS : A BRIEF OVERVIEW

In §3, we established that geospatial data generally exhibit spatial correlations and data gaps, even

when target use areas Dare small. It is well documented that calculating accuracy indices with

non-spatial validation methods (e.g. standard k-fold cross-validation) will generally over-estimate

performance in such settings. Spatially-aware evaluation methods can control the spatial distribution

of training and validation set points to better simulate conditions of intended model use.

4.1 S PATIAL CROSS -VALIDATION METHODS

Several spatial cross-validation methods have been proposed that reduce spatial dependencies be-

tween train set points ℓ∈S trainfrom evaluation set points ℓ∈S eval. Spatial cross-validation methods

3

Accepted as a paper at ICLR 2023 Workshop on Machine Learning for Remote Sensing

typically stratify training and evaluation instances by larger geographies (Roberts et al., 2017; Valavi

et al., 2018) e.g. existing boundaries, spatial blocks, or automatically generated clusters. Buffered

cross-validation methods (such as spatial leave-one-out (Le Rest et al., 2014), leave-pair out (Airola

et al., 2019) and k-fold cross validation (Pohjankukka et al., 2017)) control the minimum distance

from any training point to any evaluation point. In addition to evaluating model performance, spa-

tial cross-validation has also been suggested as a way to to improve model selection and parameter

estimation in geospatial ML (Meyer et al., 2019; Schratz et al., 2019; Roberts et al., 2017).

While separating ℓ∈S trainfromℓ∈S evalcan reduce the amount of correlation between training and

evaluation data, a spatial split also induces a higher degree of spatial extrapolation to the learning

setup and potentially reduces variation in the evaluation set labels. As a result, it is possible for

spatial validation methods to systematically under-report performance, especially in interpolation

regimes (Roberts et al., 2017; Wadoux et al., 2021). In a different ﬂavor from the evaluation methods

above, Mil `a et al. (2022) propose to match the distribution of nearest neighbor distances between

train and evaluation set points to the corresponding distances between train set and target use area.

4.2 O THER SPATIALLY -AWARE VALIDATION EVALUATION METHODS

When the intended use of a geospatial model is to generate predictions outside the training distribu-

tion, it is critical to test the model’s ability to generalize across different conditions. For example,

studies have varied the amount of spatial extrapolation required by changing parameters of the spa-

tial validation setups in §4.1 , e.g. with buffered leave one out (Ploton et al., 2020; Brenning, 2022)

and checkerboard designs (Roberts et al., 2017; Rolf et al., 2021). Jean et al. (2016) assess extrapola-

tion ability across pairs of countries by iteratitvely training in one region and evaluating performance

in another. Rolf et al. (2021) ﬁnd that the distances at which a geospatial model has extrapolation

power can differ substantially depending on the properties of the prediction variable.

It is always critical to put the reported performance of geospatial ML models in context. Visualizing

the spatial distributions of predictions and error residuals can help expose overreliance on spatially

correlated predictors (Meyer et al., 2019) and sub-regions with low local model performance. Com-

paring performance to that of a baseline model built entirely on spatial predictors can contextualize

the value-add of a new geospatial model (Fourcade et al., 2018; Rolf et al., 2021).

5 T AKING STOCK : CONSIDERATIONS AND OPPORTUNITIES

Comprehensive reporting of performance is critical for geospatial ML methods, especially as stated

gains in research progress make their way to maps and decisions of real-world consequence. Eval-

uating performance of geospatial models is especially challenging in the face of spatial correlations

and limited availability or representivity of data. This means non-spatial data splits are generally

unsuitable for geospatial model evaluation with most existing datasets. Spatially-aware validation

methods are an important indicator of model performance including spatial generalization; however,

they generally do not provide valid statistical estimates of prediction map accuracy. This brings us

to end with three key opportunities for improving the landscape of geospatial ML evaluation:

Opportunity 1: Invest in evaluation data to measure map accuracy and overall performance of

geospatial models. When remote annotations are appropriate, labeling tools (e.g. Robinson et al.

(2022)) can facilitate the creation of probability-sampled evaluation datasets. Data collection and

aggregation efforts can focus on ﬁlling existing geospatial data gaps (Paliyam et al., 2021) or simu-

lating real-world prediction conditions like covariate or domain shift (Koh et al., 2021).

Opportunity 2: Invest in evaluation frameworks to precisely and transparently and report perfor-

mance and valid uses of a geospatial ML model ( `a la “model cards” (Mitchell et al., 2019)). This

includes improving spatial baselines, expanding methods for reporting uncertainty over space, and

delineating “areas of applicability” for geospatial models, e.g. as in Meyer & Pebesma (2022).

Opportunity 3: If the available data and evaluation frameworks are insufﬁcient, explain the limita-

tions of what types of performance can be evaluated . Distinguish between performance measures

that estimate a statistical parameter and those that indicate potential skill for a possible use case.