dataesr/scientific-paragraphs-categorization huggingface dataset:
2 mm. The absence of detected deformation by Sentinel-1 in the same time interval (December 2017-December 2020) indicates that this deep source of deformation was not associated with a substantial counterpart at shallow depth. with a shallow vertical dyke, starting at a depth of 0. 7 km and reaching the surface along a 0. 6 km long north-south-oriented crack, with a volume of 0. 06 × 10 6 m 3. This has been ascribed to syneruptive dome extrusion. The longer wavelength and time period (one year) covered by ALOS-2 radar provide an opportunity to investigate whether an additional deformation source can be unpicked from InSAR data pre-eruption. In this regard, we first remove the expected deformation caused by the shallow intrusion using a forward model and the dyke parameters detailed in Joseph et al.
GI4: syn-eruptive (explosive) deflation The improved station density existing during the explosive phase allowed more source geometries to be tested. Here, using only GPS data, we apply a Bayesian approach implemented with open-source Geodetic Bayesian Inversion Software (GBIS)  (Bagnardi and Hooper 2018) , testing point (Mogi Note: Optimal is from the maximum a posteriori probability solution. The percentages 2. 5% and 97. 5% are the lower and upper boundaries of the 95% credible intervals. Lower and Upper are the bounds of the prior distribution used for the inversion. X and Y are the local coordinates of the source. Depth is positive downward. ΔV is the volume change. Ax is the length of the major semi-axis of the ellipsoid. a/r is the dimensionless aspect ratio between semi-axis (minor/major).
SVGF's atypical behaviour La Soufrière's northernmost cGPS station, SVGF (Fig. 1 ), was distinctive in increasing its horizontal motion just before the explosive phase and expanding away from the volcano after the 2020-21 eruption had ended (Fig. 5b ). Here, we speculate as to the reasons for this curious behaviour. Out of all the stations deployed during the effusive phase, SVGF was the last to be completed (Fig. 2 ) and the only monument-style installation (Fig. 3c ) (SVGS is excluded from this since it went offline shortly after it was installed). It is therefore probable that data recorded by SVGF reflect the coinciding effects of concrete settling and magma withdrawal. SVGF's time-series post-eruptive trajectory may also underscore some of La Soufrière's structural heterogeneities. Its edifice consists of an older stratocone or Somma, within which a younger pyroclastic cone emerges that has been the source of historical eruptions  (Robertson 2005).
If this was indeed a definitive signal, the pressure source responsible for this change might have been characterized had the summit station (SVGS) been operational and/or satellite repeat times for longer wavelength radar (ALOS-2 and SAOCOM) been similar to this deformation timescale. Once the explosions began, the extremely heavy ash fall and destruction of the crater area made it impossible to obtain coherent interferograms from post-explosive phase ALOS-2 (Fig. S6 ) and Sentinel-1 images. SAOCOM radar conversely was able to detect the syn-eruptive (explosive) deflation also measured by the cGPS network (Fig. 7 ). GPS instrumentation was also affected by ashfall with recording interruptions and the addition of noise to the data (Fig. 5 ). Overall, our retrospective analysis of GPS and InSAR data reveals the wealth of information that could have been utilized before and during this eruption had they both been optimized/available in real time.
First, it focuses on compliance with the European supranational fiscal rules of the SGP (1996) using machine learning. Macroeconomic studies involving machine learning methods are still rare in the literature but are becoming increasingly popular (see e. g. Medeiros et al. , 2021; Gogas et al. , 2022; Yoon, 2021). The use of machine learning to study SGP compliance is original. Second, the proposed method can handle the size limitation of datasets often encountered in macroeconomics studies. While early machine learning algorithms required extensive datasets that are typically unavailable in economics (with the exception of finance), many newer machine learning architectures (such as support vector machines (SVM), Random Forests, and various boosting-based methods) have more accessible data requirements and offer an interesting avenue in economic forecasting.
This paper fits into the latter strand of literature. Thus, we assume that: (i) the existence of fiscal rules is justified (see for instance  Debrun et al. (2008)  or  Wyplosz (2012)  for a general overview of the main reasons for introducing fiscal rules) and (ii) that the applied quantitative limits are optimal. It is not the purpose of this paper to question these assumptions. There have been many studies of fiscal rule compliance. Some assess levels of compliance with fiscal rules based on fiscal rule databases maintained by the EU Commission (2017) or the IMF (2016). 15  These databases provide information on the fiscal rule and its coverage, its statutory base, monitoring bodies, correction mechanisms in cases of deviation, and records of compliance with the rule. Composite indicators have been defined based on these data to assess the potential coercive power of fiscal rules (see for instance, the European Commission's or the IMF's Fiscal Rule Index (FRI)  16  ).
| Fiscal rule compliance: potential predictors We tried to assemble a dataset covering all the relevant features for forecasting SGP compliance. These variables are listed in contains complete series for many macroeconomic variables. Nevertheless, the MIP scoreboard was not designed to forecast SGP compliance. We therefore also include other variables. Variables X1 to X6 are economic integration indicators: dummy variables for the country's status as an advanced or an emerging economy (X1 and X2); a dummy variable indicating whether the country was an EU Member (X3), and a dummy variable reflecting a country's federal nature (X4). A dummy variable indicating whether or not the country was a eurozone member (X5) is included to test whether eurozone members comply with the rule more often than non-members.
The European Commission's FRSI quantifies the strength of all national (and subnational) fiscal rules by applying a standardisation procedure to these scores. In short, while the FRSI measures the strength of each fiscal rule separately, the FRI (used in our study) represents the strength index of all fiscal rules at all levels of government in a given country. We thus include the FRI (X45) to see whether countries that also implement strong national fiscal rules are more likely to comply with the 3% rule of the SGP. Finally, following  Annett (2000)  and using the World Bank's Database of Political Institutions, variable X46 measures the level of government fragmentation in each country, as reflected by the dispersion of parties in parliament. 29 We want to see if government fragmentation is related to SGP compliance.
Y is our binary dependent variable describing a country's compliance with the SGP (3% limit) in year t. Our aim is to forecast Y t using lagged values of the 46 variables in the dataset X i,j , i = 1,. , 46, j = t -1, t -2, t -3. Y is the Dependent variable. The X variables are the 28 An index ranging from 1 to 21 from the World Bank's 'Cross-Country Database of Fiscal Space'  (Ayhan Kose et al. , 2017). 29 We used the  Annett (2000)  definition of society fractionalisation applied to government fractionalisation: Fractionalisation = 1 - ∑ M i=1 � n i N � 2 i = 1,. , M with N being the total number of seats in a country's parliament and n i is the number of seats belonging to the i-th party. Government fractionalisation is thus defined as the probability that two randomly chosen members of parliament come from two different parties (which also corresponds to the World Bank definition of government fragmentation).
| EMPIRICAL STRATEGY We performed three sets of tests, comparing in each case the best SVM model with the best logit model on the same dataset. We first included just the main indicators of the MIP scoreboard, to check whether these variables, designed to prevent internal and external imbalances, might also be relevant to SGP compliance. We then tested our framework using the complete dataset presented in Table  2. The second model outperforming the first would therefore indicate that the MIP scoreboard is insufficient to forecast SGP compliance. In the third set of tests, we combined a well-established feature selection method with our forecasting scheme, to select only the necessary variables in the model.
| The logistic function We used a traditional econometric method (logit regression) and an emerging approach in economics from the field of machine learning (support vector machine), with the aim of creating the most accurate forecasting model by comparing the two. The logistic function is commonly used for forecasting purposes, as for instance by  Martin (1977)  and  Olson (1980) , who used logistic regression to forecast bank and firm failures. Our forecasting problem can be viewed as one of binary classification: to predict whether the countries in the dataset will comply with the rule (class 1) or not (class 0) Y ∈ {0; 1}. The goal of our system is to use the input variables to find the linear or non-linear separator that correctly classifies the cases. The collected data are represented by x i,j , i = 1, ⋯ , n and j = 1, ⋯ , m, describing n = 364 data points with m = 138 features, arranged in vectors x i = [x i,1 , ⋯ , x i,138 ] T.
The logistic function constrains Y to the range (0, 1) via the sigmoid function: where x i = [1, x T i ] T corresponds to a feature-column (the 1 corresponds to the intercept of the regression) and is the column vector of the regression coefficients. The classifier produces a probability score between 0 and 1, with values lower than 0. 5 corresponding to class 0; and probabilities of 0. 5 or above corresponding to class 1. The goal is to find the according to p(Y |X ) that most accurately classifies the observed data points. The problem is equivalent to maximising the product of the likelihood probabilities: (1) The SVM algorithm for linearly separable data SVM is a supervised machine learning method 30 for the binary classification of a set of data points. SVM aims at identifying a small subset of data points from the initial dataset, called support vectors, that define the position of the linear separator between the two classes.
, a n ] T are the non-negative Lagrange multipliers. (  4 ) is not used to calculate the solution. Instead the simpler dual problem is solved, described by: with ∑ N i=1 a i y i = 0 and 0 ≤ a i , ∀ i. The location of the hyperplane is obtained by solving (5), leading to: where V = {i: 0 < a i } is the set of support vector indices. To account for noise and outliers in the dataset,  Cortes and Vapnik (1995)  introduced non-negative slack variables i ≥ 0, ∀ i that are tolerant of a certain level of misclassification. To keep the misclassification rate as low as possible, each misclassification is counted as an additional cost in the objective function to be minimised. where the non-negative slack i correspond to the distance of vector x i from the hyperplane when classified erroneously. k = [ 1 ,.
| Feature selection: logistic LASSO regression The goal of feature selection is to reduce the input set by removing irrelevant or redundant features in the model. Reducing the input set decreases the computational cost of training and limits the risk of overfitting. Friedman et al. (2009)  proposed LASSO as an alternative regularisation method in cases where ridge regression fails to reduce the number of predictors in the model. LASSO involves penalising the coefficients of some of the input variables and shrinking them to zero. The main goal of the method is to minimise the prediction error, yielding selected features among the variables as a by-product. The shrinkage operation identifies the key features in the dataset, avoiding the problems associated with transformation-based dimension reduction approaches such as factor analysis, principal component analysis and independent component analysis, whose factors are uninterpretable.
| Assessment of forecasting performance The performance of our models was calculated as the proportion of correctly forecasted observations: where TP is the number of true positives (correctly forecasted positive instances), TN is the number of true negatives (correctly forecasted negative instances), FP is the number of false positives (incorrectly forecasted positive instances), and FN is the number of false negative instances (incorrectly forecasted negative instances). Note that in our setup, a positive (negative) instance is a member state that respected (broke) the rule in year t. The forecasting accuracy is a simple and easy-to-use metric but is somewhat coarse and superficial. Consider, for example, a dataset of 90 positive and 10 negative cases, analysed using a naive model yielding only positive forecasts.
| Validation Machine learning methods are, in general, unaffected by reverse causality, which is a common problem in classic econometrics. They are liable to overfitting, however, a common error whereby the model learns to describe the training data instead of the underlying phenomenon. Overfitting can be avoided by performing hold-out validation or the more powerful k-fold cross-validation (see Figure  3  for illustration). In hold-out validation, the dataset is split into a 'training' set and 'test' set. The model is trained on the training set and the test set is used to evaluate the performance of the model on unknown data. If the training accuracy is much higher than the testing accuracy, this is a strong indication that the model overfitted the training dataset. Typically, around 80% of the data is used for training and 20% for testing.
The k-fold cross-validation involves repeating the process k times on k equally sized subsets. 32 A different subset is used as the 'test' set in each run, and the remaining k-1 subsets constitute the 'training' set. The average performance over the k runs is used to select the optimal model. Figure  3  provides an illustration of iterations of a 5-fold cross validation process. In each iteration, a different chunk of the dataset is used for testing (show in red), while the remaining four parts are used for training (green). In each iteration, the position of the separator is fixed using the training subset, and the model is evaluated using the testing subset. The overall performance of the model is quantified by the mean classification error over the five iterations.
| Forecasting SGP compliance We tested the SVM classification algorithm with three kernels (linear, RBF and polynomial) and used the performance of the logistic regression model on the same datasets as a benchmark. In a first stage, the models were trained using the primary indicators of the MIP scoreboard to 32 The appropriate value of k is somewhat arbitrary. Yadav and Shukla (2016)  found that k = 10 was suitable for a large dataset and that k=2 produced and underfitted model, whereas  Chernozhukov et al. (2018)  found that k = 2 and k = 5 led to similar results. Given the limited size of our dataset, k = 5 seems a reasonable choice. T A B L E 3 'Compliance with 3% limit' forecasting accuracy: comparison of models (%). evaluate the potential of the MIP scoreboard variables to forecast compliance with the 3% rule.
The training process was then repeated using the entire 138-variable dataset. The results of these two analyses are reported in Table  3. The results obtained with the two datasets show that in almost every case, the models trained with the full dataset outperformed those trained on the primary MIP scoreboard only. The highest prediction accuracy with the MIP scoreboard variables (85. 1%) was achieved with the linear kernel SVM model and hold-out validation (the corresponding accuracy with the full dataset was 87%). With the full dataset, the SVM models with non-linear kernels (the quadratic and the RBF kernel) had a forecasting accuracy of 88. 9% in hold-out cross-validation, the best performance achieved with any of the models in hold-out validation. The gains in performance of the models trained on the full dataset were more substantial in k-fold cross-validation: the accuracy of the models trained on the restricted set ranged from 62.
9% with the RBF-SVM model, to 69. 5% for the quadratic kernel SVM model, whereas for the models trained on the full dataset ranged forecasting accuracies ranged from 75. 5% for the logit model to 83. 5% for the linear SVM model. These results suggest that the full dataset has a greater forecasting power than the primary MIP scoreboard indicators alone. The next step of our study was to identify the optimal input dataset using LASSO-based feature selection. LASSO feature selection 33  highlighted the 12 key variables for forecasting SGP compliance. Following  Gogas et al. (2018) , these variables were introduced into the SVM forecasting model and the input dataset was further shrunk by comparing the results with all 12 selected variables with those obtained when each of these variables was removed in turn.
The optimal set was retained and the procedure was repeated until no improvement was achieved. The final dataset consisted of eight features: (a) the general government fiscal balance in period t -1 (as expected since a weak fiscal balance in one year will tend to affect the next), (b) financial sector liabilities in period t -1 (the global financial crisis highlighted the interdependence of finan- cial institutions, their liabilities and public finance sustainability); 34  the dummy variables reflecting the occurrence of a crisis in periods t -1 and t -2; economic crises indeed have a dual impact on public deficits: they induce economic recessions and increase investment needs (furthermore, the fact that these two features are identified as crucial indicates that the SGP escape clause should account for the length of crises and not just focus on drops in GDP during recessions), (d) the output gap in period t -1 (the output gap is an indicator of position in the economic cycle-increased GDP volatility under poor economic conditions impacts public deficit and thus SGP compliance), (e) oil prices in period t -1 (increases in oil prices have led to crises directly, as in 1973 and 1979, or by proxy, as in 2008-the 'yellow vests' movement, triggered in 2018 by oil prices in France, is a further example of the consequences on public deficits that these situations can have), (f) the bond yield in period t -1 and (g) the fiscal space in period t -1 (both variables are measures of government fiscal flexibility, especially in periods of crises-this is in line with  Romer and Romer (2018) , who highlight the importance of fiscal space during financial crises and normal recessions).
This is not the case for public debt, which is at the heart of the third reform of the SGP and takes much longer to rectify. We identified a set of 8 features from a dataset of 138 variables using LASSO feature selection, and compared results from SVM models with three different kernels, using a logit model as a benchmark. The best results were obtained with the linear kernel SVM model, which when trained with a k-fold cross-validation setup had a forecasting accuracy of 91. 7% (accurately forecasting 112 out of the 135 cases of non-compliance and 222 out of the 229 cases of compliance). Our findings contribute to several areas of research: First, they feed the discussion on 'the impact of Machine Learning on economics'  (Athey, 2018). Indeed, machine learning models provide high forecasting power, and should be considered in fiscal policy outcome forecasting and risk prevention.
Third, there are several possibilities for future research: (i) this approach could be used with the Compliance Tracker Database  (Larch and Santacroce, 2020)  to analyse compliance with the other fiscal rules in the SGP, such as the structural balance rule and the expenditure rule; (ii) the model could also be applied to forecast compliance with national fiscal policy outcomes using national-level datasets; (iii) these models could also be applied to other macroeconomic outcomes and forecast compliance with other objectives, in monetary and macroprudential policy for instance.
14679701, 2024, 1, Downloaded from https://onlinelibrary. wiley. com/doi/10. 1111/twec. 13518 by Cochrane France, Wiley Online Library on [03/05/2024]. See the Terms and Conditions (https://onlinelibrary. wiley. com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License having been placed under strict European Commission monitoring for 10 years following the Sovereign Debt Crisis. Figure5shows 1 5 of the dataset 36 and the linear separator hyperplane. 37 The red dots circled in purple are the instances of non-compliance that are closest to the hyperplane (e. g. Belgium in 2014 and Croatia in 2012) and therefore would have been the easiest to rectify. The black dots circled in purple would also have triggered increased attention because they are close to the 'cliff edge' (the Slovak Republic in 2007 for example).
Primary MIP scoreboard variables only All features (138) Primary MIP scoreboard variables only All features (138) [Colour table can be viewed at wileyonlinelibrary. com]Note: Hold-out splits the dataset into a 'training set' (85%) and a 'test set' (15%). The results are from the test set. For k-fold cross-validation the process was repeated 5 times; the values shown are the mean results. Parameter C in the SVM algorithm is equal to 2 1 and was obtained using a power-of-2 grid search. Best accuracy results are highlighted in yellow. Model Linear SVM model 64. 6 83. 5 85. 1 87. 0 Quadratic SVM model 69. 5 83. 0 79. 6 88. 9 RBF SVM model 62. 9 80. 2 77. 8 88. 9 Logistic model 63. 7 75. 5 75. 9 73. 3 Cross-validation method k-Fold k-fold Hold-out Hold-out.
4 98. 1 Quadratic SVM model 84. 6 87. 0 RBF SVM model ( = 12) 86. 5 88. 9 Logistic model 78. 5 76. 3 Cross-validation method k-fold Hold-out Note: Hold-out splits the dataset into a 'training set' (85%) and a 'test set' (15%). 14679701, 2024, 1, Downloaded from https://onlinelibrary. wiley. com/doi/10. 1111/twec. 13518 by Cochrane France, Wiley Online Library on [03/05/2024]. See the Terms and Conditions (https://onlinelibrary. wiley. com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License forecasting model derived.
of mitigation actions, for cost-effectiveness and to maximize emission reduction impact, depends mainly on the qualitative and quantitative understanding of urban emission sources with temporal-spatial details to understand evolving emission trends  (Lauvaux et al. , 2020; Mueller et al. , 2021). However, the bottom-up carbon emissions based on public protocols for cities are prone to large uncertainties  (Gurney et al. , 2021). High-resolution gridded CO2 emission inventories, e. g. , the Hestia dataset for some US cities  (Gurney et al. , 2019)  or the LAEI dataset for Greater London (Greater London Authority, 2021), could provide a 5 detailed description of emissions from urban domains. This approach relies on a collection of extensive activity data and emission factors, and thus can be labor-intensive and time-consuming, especially for doing regular updates.