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Publication: Adding the spatial dimension to the assessment of predictive performance of and variable importance in statistical and machine-learning models

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Title Adding the spatial dimension to the assessment of predictive performance of and variable importance in statistical and machine-learning models
Authors/Editors* A. Brenning
Where published* Abstracts, Down to Earth, IGC Cologne 2012, 32nd International Geographical Congress, Köln, 26-30 August 2012
How published* Proceedings
Year* 2012
Tapping the potential of predictive methods developed in the fields of computational statistics and machine learning in geographical applications has just recently begun. While these relatively novel methods offer new opportunities for modeling nonlinear and interactive relationships and dealing with high-dimensional problems, new challenges as well as opportunities arise due to the presence of spatial autocorrelation in geospatial data. Spatial resampling-based methods (cross-validation, bootstrap) have recently been proposed to assess the performance of such complex models in supervised spatial classification and regresssion, revealing in some geospatial applications a lack of spatial transferability due to overfitting. Similarly, permutation-based measures of variable importance have been adapted to the context of spatial prediction using spatial resampling, providing a focused assessment of the utility of predictor variables in spatial modeling. This contribution extends this approach to exploring resampling-based predictive performance and variable importance as a function of distance between training and test samples. This creates a novel tool for the explicitly spatial assessment of prediction models as well as for the characterization of spatial variables. The tool is applied to landslide susceptibility modeling, remotely-sensed land cover classification and spatial interpolation in precision agriculture. In spatial interpolation, the proposed computational measures are compared to traditional geostatistical approaches, specifically the semivariogram for characterizing spatial relationships, and the kriging variance for quantifying predictive uncertainty. It is concluded that the proposed novel spatial accuracy assessment and variable importance tools provide insights that were previously only available in the narrow context of parametric geostatistical methods, and offers these insights in the broader contexts of supervised classification, regression and interpolation. The proposed methods are also relevant to other situations in which autocorrelation occurs in a continuous or discrete space, such as time series, lattice data and data on networks.
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