Random forest as a generic framework for predictive modeling of spatial and spatio-temporal variables

By Tomislav Hengl, Madlene Nussbaum, Marvin N. Wright, Gerard B. M. Heuvelink, Benedikt Gräler. PeerJ, 2018

919 citations recorded by the source corpus.

Random forest and similar Machine Learning techniques are already used to generate spatial predictions, but spatial location of points (geography) is often ignored in the modeling process. Spatial auto-correlation, especially if still existent in the cross-validation residuals, indicates that the predictions are maybe biased, and this is suboptimal. This paper presents a random forest for spatial predictions framework (RFsp) where buffer distances from observation points are used as explanatory variables, thus incorporating geographical proximity effects into the prediction process. The RFsp framework is illustrated with examples that use textbook datasets and apply spatial and spatio-temporal prediction to numeric, binary, categorical, multivariate and spatiotemporal variables. Performance of the RFsp framework is compared with the state-of-the-art kriging techniques using fivefold cross-validation with refitting. The results show that RFsp can obtain equally accurate and unbiased predictions as different versions of kriging. Advantages of using RFsp over kriging are that it needs no rigid statistical assumptions about the distribution and stationarity of the target variable, it is more flexible towards incorporating, combining and extending covariates of different types, and it possibly yields more informative maps characterizing the prediction error. RFsp appears to be especially attractive for building multivariate spatial prediction models that can be used as “knowledge engines” in various geoscience fields. Some disadvantages of RFsp are the exponentially growing computational intensity with increase of calibration data and covariates and the high sensitivity of predictions to input data quality. The key to the success of the RFsp framework might be the training data quality—especially quality of spatial sampling (to minimize extrapolation problems and any type of bias in data), and quality of model validation (to ensure that accuracy is not effected by overfitting). For many data sets, especially those with lower number of points and covariates and close-to-linear relationships, model-based geostatistics can still lead to more accurate predictions than RFsp.

Subfields: Economics and Econometrics, Environmental Engineering, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/37ed0bde01a492738b8779c613d9f23500bdc318

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Citations in the corpus

Random Forests for dependent data (2020, background): “[37] considered a direct spatial RF for predicting yi by adding as additional predictors the pairwise distances between the location `i and the other locations in the RF.”
Predicting the trend of indicators related to Covid-19 using the combined MLP-MC model (2021, neutral): “[38] Hengl T, Nussbaum M, Wright MN, Heuvelink GBM, Gräler B.”
Importance of spatial predictor variable selection in machine learning applications - Moving from data reproduction to spatial prediction (2019, background): “Distances to certain points (e.g. Hengl et al., 2018) or Euclidean distance to the corner coordinates of the model domain (e.g. Behrens et al., 2018) have also been suggested as predictors and included in models.”
Geographical random forests: a spatial extension of the random forest algorithm to address spatial heterogeneity in remote sensing and population modelling (2019, methodology): “Finally, including the geographical coordinates as features appears to be a good practice when using ML algorithms with spatial data, con ﬁ rming prior research (Hengl et al. 2018).”
Predicting into unknown space? Estimating the area of applicability of spatial prediction models (2020, background): “…is also not addressed by the quantile regression forests (Meinshausen, 2006) that are occasionally suggested in the context of spatial mapping (Hengl et al., 2018; Vaysse and Lagacherie, 2017) to derive prediction intervals based on the conditional distribution of the response variable.”
Random Forest Spatial Interpolation (2020, methodology): “We would also like to thank Tom Hengl and co-authors [8,26] for their reproducible research paper, the R-sig-geo community for developing free and open tools for space–time modeling and all researchers [34] and developers [43,44] that made RFSI modelling in R possible.”