Gaussian Processes for vegetation traits global mapping

Machine learning algorithms have become widely used for geospatial applications, including spatial mapping and upscaling ecological variables and traits. Multivariate splines, random forests, and neural networks have been widely used to upscale a few sparse measurements to larger areas. Machine learning models, however, cannot offer reliable predictions in out-of-the-sample areas, which is often the case in such applications [1,2]. In [3], an area of applicability is proposed as an extrapolation index based on the minimum distance to the training data in the multidimensional predictor space with predictors being weighted by their respective importance in the model. We propose Gaussian Processes (GPs) to derive such extrapolation indicator [4].  A GP is a popular method in machine learning and multivariate statistics for regression problems. It provides a probabilistic description of the predictive function, so one can derive both predictive mean and variance for the predictions on new data. We here suggest using the predictive variance as an indicator for extrapolation and show the relation with a customized dissimilarity index computed that follows the Area of Applicability methodology proposed in [3]. We show the relation and in some cases the generalization in a set of controlled synthetic experiments and for vegetation traits global mapping using remote sensing, meteorological variables and the (huge yet sparse and biased) TRY database. This relation opens the door to a more sound way of identifying and characterizing extrapolation regimes through GPs in geospatial and upscaling applications.

References

[1] Deep learning for the Earth Sciences: A comprehensive approach to remote sensing, climate science and geosciences. Gustau Camps-Valls, Devis Tuia, Xiao Xiang Zhu, Markus Reichstein (Editors). Wiley & Sons 2021

[2] Perspective on Deep Learning for Earth Sciences. Camps-Valls, Gustau. Generalization with Deep Learning: for Improvement on Sensing Capability, World Scientific Pub Co Inc 2021

[3] Meyer, H., & Pebesma, E. (2021). Predicting into unknown space? Estimating the area of applicability of spatial prediction models. Methods in Ecology and Evolution, 12, 1620–1633. https://doi.org/10.1111/2041-210X.13650

[4] A Survey on Gaussian Processes for Earth Observation Data Analysis: A Comprehensive Investigation. Camps-Valls, G. and Verrelst, J. and Muñoz-Marí, J. and Laparra, V. and Mateo-Jiménez, F. and Gómez-Dans, J. IEEE Geoscience and Remote Sensing Magazine 2016