Random Forests for Spatially Dependent Data

References

• Ahijevych, D., Pinto, J. O., Williams, J. K., and Steiner, M. (2016), “Probabilistic Forecasts of Mesoscale Convective System Initiation Using the Random Forest Data Mining Technique,” Weather and Forecasting, 31, 581–599.
   Web of Science ®Google Scholar
• Banerjee, S., Carlin, B. P., and Gelfand, A. E. (2014), Hierarchical Modeling and Analysis for Spatial Data, Boca Raton, FL: CRC Press.
   Google Scholar
• Bradley, R. C. (2005), “Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions,” arXiv: math/0511078.
   Google Scholar
• Breiman, L. (1996), “Bagging Predictors,” Machine Learning, 24, 123–140. DOI: 10.1007/BF00058655.
   Web of Science ®Google Scholar
• Breiman, L. (2001), “Random Forests,” Machine Learning, 45, 5–32.
   Web of Science ®Google Scholar
• Breiman, L., Friedman, J., Stone, C. J., and Olshen, R. A. (1984), Classification and Regression Trees, Boca Raton, FL: CRC Press.
   Google Scholar
• Carrasco, M. and Chen, X. (2002), “Mixing and Moment Properties of Various GARCH and Stochastic Volatility Models,” Econometric Theory, 17–39. DOI: 10.1017/S0266466602181023.
   Web of Science ®Google Scholar
• Chen, Y. M., Chen, X. S., and Li, W. (2016), “On Perturbation Bounds for Orthogonal Projections,” Numerical Algorithms, 73, 433–444. DOI: 10.1007/s11075-016-0102-2.
   Web of Science ®Google Scholar
• Datta, A., Banerjee, S., Finley, A. O., and Gelfand, A. E. (2016a), “Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets,” Journal of the American Statistical Association, 111, 800–812. DOI: 10.1080/01621459.2015.1044091.
   PubMed Web of Science ®Google Scholar
• Datta, A., Banerjee, S., Finley, A. O., and Gelfand, A. E. (2016b), “On Nearest-Neighbor Gaussian Process Models for Massive Spatial Data,” Wiley Interdisciplinary Reviews: Computational Statistics, 8, 162–171.
   PubMedGoogle Scholar
• Datta, A., Banerjee, S., Finley, A. O., Hamm, N. A. S., and Schaap, M. (2016c), “Nonseparable Dynamic Nearest Neighbor Gaussian Process Models for Large Spatio-Temporal Data With an Application to Particulate Matter Analysis,” Annals of Applied Statistics, 10, 1286–1316.
   PubMed Web of Science ®Google Scholar
• Dehling, H., and Philipp, W. (2002), “Empirical Process Techniques for Dependent Data,” in Empirical Process Techniques for Dependent Data, Boston, MA: Springer, pp. 3–113.
   Google Scholar
• Di, Q., Amini, H., Shi, L., Kloog, I., Silvern, R., Kelly, J., Sabath, M. B., Choirat, C., Koutrakis, P., Lyapustin, A., et al. (2019), “An Ensemble-Based Model of PM2. 5 Concentration Across the Contiguous United States with High Spatiotemporal Resolution,” Environment International, 130, 104909. DOI: 10.1016/j.envint.2019.104909.
   PubMed Web of Science ®Google Scholar
• Diggle, P. J., and Hutchinson, M. F. (1989), “On Spline Smoothing With Autocorrelated Errors,” Australian Journal of Statistics, 31, 166–182. DOI: 10.1111/j.1467-842X.1989.tb00510.x.
   Google Scholar
• Doukhan, P. (2012), Mixing: Properties and Examples, Vol. 85, New York: Springer Science & Business Media.
   Google Scholar
• Du, J., Zhang, H., Mandrekar, V., et al. (2009), “Fixed-Domain Asymptotic Properties of Tapered Maximum Likelihood Estimators,” The Annals of Statistics, 37, 3330–3361. DOI: 10.1214/08-AOS676.
   Web of Science ®Google Scholar
• Fayad, I., Baghdadi, N., Bailly, J.-S., Barbier, N., Gond, V., Hérault, B., El Hajj, M., Fabre, F., and Perrin, J. (2016), “Regional Scale Rain-Forest Height Mapping Using Regression-Kriging of Spaceborne and Airborne LiDAR Data: Application on French Guiana,” Remote Sensing, 8, 240. DOI: 10.3390/rs8030240.
   Web of Science ®Google Scholar
• Finley, A. O., Datta, A., and Banerjee, S. (2021), “spNNGP: R package for Nearest Neighbor Gaussian Process Models,” Journal of Statistical Software, (accepted conditionally).
   PubMed Web of Science ®Google Scholar
• Finley, A. O., Datta, A., Cook, B. D., Morton, D. C., Andersen, H. E., and Banerjee, S. (2019), “Efficient Algorithms for Bayesian Nearest Neighbor Gaussian Processes,” Journal of Computational and Graphical Statistics, 28, 401–414. DOI: 10.1080/10618600.2018.1537924.
   PubMed Web of Science ®Google Scholar
• Fox, E. W., Ver Hoef, J. M., and Olsen, A. R. (2020), “Comparing Spatial Regression to Random Forests for Large Environmental Data Sets,” PloS One, 15, e0229509. DOI: 10.1371/journal.pone.0229509.
   PubMed Web of Science ®Google Scholar
• Friedman, J., Hastie, T., and Tibshirani, R. (2001), The Elements of Statistical Learning, Vol. 1, New York: Springer Series in Statistics.
   Google Scholar
• Friedman, J. H. (1991), “Multivariate Adaptive Regression Splines,” The Annals of Statistics, 1–67. DOI: 10.1214/aos/1176347963.
   Web of Science ®Google Scholar
• Friedman, J. H. (2006), “Recent Advances in Predictive (Machine) Learning,” Journal of Classification, 23, 175–197.
   Web of Science ®Google Scholar
• Friedman, J. H., Popescu, B. E., et al. (2008), “Predictive Learning via Rule Ensembles,” The Annals of Applied Statistics, 2, 916–954. DOI: 10.1214/07-AOAS148.
   Web of Science ®Google Scholar
• Genton, M. G. and Kleiber, W. (2015), “Cross-Covariance Functions for Multivariate Geostatistics,” Statistical Science, 147–163. DOI: 10.1214/14-STS487.
   Web of Science ®Google Scholar
• Georganos, S., Grippa, T., Niang Gadiaga, A., Linard, C., Lennert, M., Vanhuysse, S., Mboga, N., Wolff, E., and Kalogirou, S. (2019), “Geographical Random Forests: A Spatial Extension of the Random Forest Algorithm to Address Spatial Heterogeneity in Remote Sensing and Population Modelling,” Geocarto International, 1–16. DOI: 10.1080/10106049.2019.1595177.
   Web of Science ®Google Scholar
• Györfi, L., Kohler, M., Krz.yzak, A., and Walk, H. (2002), A Distribution-Free Theory of Nonparametric Regression (Vol. 1), New York: Springer.
   Google Scholar
• Hartikainen, J., and Särkkä, S. (2010), “Kalman Filtering and Smoothing Solutions to Temporal Gaussian Process Regression Models,” in 2010 IEEE International Workshop on Machine Learning for Signal Processing, Kittilä, Finland, IEEE, pp. 379–384.
   Google Scholar
• Heaton, M. J., Datta, A., Finley, A. O., Furrer, R., Guinness, J., Guhaniyogi, R., Gerber, F., Gramacy, R. B., Hammerling, D., Katzfuss, M., Lindgren, F., Nychka, D., Sun, F., Zammit-Mangion, A. (2019), “A Case Study Competition Among Methods for Analyzing Large Spatial Data,” Journal of Agricultural, Biological and Environmental Statistics, 24, 398–425. DOI: 10.1007/s13253-018-00348-w.
   PubMed Web of Science ®Google Scholar
• Hengl, T., Nussbaum, M., Wright, M. N., Heuvelink, G. B., and Gräler, B. (2018), “Random Forest as a Generic Framework for Predictive Modeling of Spatial and Spatio-Temporal Variables,” PeerJ, 6, e5518. DOI: 10.7717/peerj.5518.
   PubMed Web of Science ®Google Scholar
• Ihara, S. (1993), Information Theory for Continuous Systems, Vol. 2, World Scientific.
   Google Scholar
• Kimeldorf, G., and Wahba, G. (1971), “Some Results on Tchebycheffian Spline Functions,” Journal of Mathematical Analysis and Applications, 33, 82–95. DOI: 10.1016/0022-247X(71)90184-3.
   Web of Science ®Google Scholar
• Lim, C. C., Kim, H., Vilcassim, M. R., Thurston, G. D., Gordon, T., Chen, L.-C., Lee, K., Heimbinder, M., and Kim, S.-Y. (2019), “Mapping Urban air Quality Using Mobile Sampling With Low-Cost Sensors and Machine Learning in Seoul, South Korea,” Environment International, 131, 105022.
   PubMed Web of Science ®Google Scholar
• Lin, Y., and Jeon, Y. (2006), “Random Forests and Adaptive Nearest Neighbors,” Journal of the American Statistical Association, 101, 578–590. DOI: 10.1198/016214505000001230.
   Web of Science ®Google Scholar
• Mentch, L., and Hooker, G. (2016), “Quantifying Uncertainty in Random Forests Via Confidence Intervals and Hypothesis Tests,” The Journal of Machine Learning Research, 17, 841–881.
   Web of Science ®Google Scholar
• Mentch, L., and Zhou, S. (2020), “Getting Better from Worse: Augmented Bagging and a Cautionary Tale of Variable Importance,” arXiv: 2003.03629.
   Google Scholar
• Mokkadem, A. (1988), “Mixing Properties of ARMA Processes,” Stochastic Processes and Their Applications, 29, 309–315. DOI: 10.1016/0304-4149(88)90045-2.
   Web of Science ®Google Scholar
• Nobel, A., and Dembo, A. (1993), “A Note on Uniform Laws of Averages for Dependent Processes,” Statistics & Probability Letters, 17, 169–172.
   Web of Science ®Google Scholar
• Nobel, A. et al. (1996), “Histogram Regression Estimation Using Data-Dependent Partitions,” The Annals of Statistics, 24, 1084–1105. DOI: 10.1214/aos/1032526958.
   Web of Science ®Google Scholar
• Pardo-Igúzquiza, E. and Olea, R. A. (2012), “VARBOOT: A Spatial Bootstrap Program for Semivariogram Uncertainty Assessment,” Computers & Geosciences, 41, 188–198.
   Web of Science ®Google Scholar
• Peligrad, M. (2001), “A Note on the Uniform Laws for Dependent Processes Via Coupling,” Journal of Theoretical Probability, 14, 979–988.
   Web of Science ®Google Scholar
• Saha, A. and Datta, A. (2018a), “BRISC: Bootstrap for Rapid Inference on Spatial Covariances,” Statistics, 7, e184. DOI: 10.1002/sta4.184.
   Web of Science ®Google Scholar
• Saha, A. and Datta, A. (2018b), BRISC: Fast Inference for Large Spatial Datasets Using BRISC, r package version 0.1.0.
   Google Scholar
• Scornet, E. (2016), “Random Forests and Kernel Methods,” IEEE Transactions on Information Theory, 62, 1485–1500. DOI: 10.1109/TIT.2016.2514489.
   Web of Science ®Google Scholar
• Scornet, E., Biau, G., and Vert, J.-P. (2015), “Consistency of Random Forests,” The Annals of Statistics, 43, 1716–1741. DOI: 10.1214/15-AOS1321.
   Web of Science ®Google Scholar
• Stein, M. L. (2012), Interpolation of Spatial Data: Some Theory for Kriging, Springer Science & Business Media. New York: Springer-Verlag.
   Google Scholar
• Stein, M. L. (2002), “The Screening Effect in Kriging,” The Annals of Statistics, 30, 298–323. DOI: 10.1214/aos/1015362194.
   Web of Science ®Google Scholar
• Taylor, J., and Einbeck, J. (2013), “Challenging the Curse of Dimensionality in Multivariate Local Linear Regression,” Computational Statistics, 28, 955–976. DOI: 10.1007/s00180-012-0342-0.
   Web of Science ®Google Scholar
• Vecchia, A. V. (1988), “Estimation and Model Identification for Continuous Spatial Processes,” Journal of the Royal Statistical Society, Series B, 50, 297–312. DOI: 10.1111/j.2517-6161.1988.tb01729.x.
   Google Scholar
• Viscarra Rossel, R. A., Webster, R., and Kidd, D. (2014), “Mapping Gamma Radiation and Its Uncertainty From Weathering Products in a Tasmanian Landscape With a Proximal Sensor and Random Forest Kriging,” Earth Surface Processes and Landforms, 39, 735–748. DOI: 10.1002/esp.3476.
   Web of Science ®Google Scholar
• Wager, S., and Athey, S. (2018), “Estimation and Inference of Heterogeneous Treatment Effects Using Random Forests,” Journal of the American Statistical Association, 113, 1228–1242. DOI: 10.1080/01621459.2017.1319839.
   Web of Science ®Google Scholar
• Zhang, H. (2004), “Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics,” Journal of the American Statistical Association, 99, 250–261. DOI: 10.1198/016214504000000241.
   Web of Science ®Google Scholar