{"refrec":{"BRefID":340821,"RR":"<b>O'Malley, M.; Sykulski, A.M.; Lumpkin, R.; Schuler, A.</b> (2021). Multivariate probabilistic regression with natural gradient boosting. <i>arXiv (Archive) 2106.03823v1</i>","BEntID":337456,"PublicFlag":1,"CheckedFlag":0,"wosflag":0,"vabbflag":0,"RefStringPartII":". <i>arXiv (Archive) 2106.03823v1</i>","DocTypID":8,"DocType":"Journal article","MarineFlag":0,"FreshFlag":0,"BrackishFlag":0,"TerrestrialFlag":0,"Authorstring":"O'Malley, M.; Sykulski, A.M.; Lumpkin, R.; Schuler, A.","OrigTitleTranslFlag":0,"Authorstringtrunc":"O'Malley, M. <i>et al.</i>","Englishabstract":"Many single-target regression problems require estimates of uncertainty along with the point predictions. Probabilistic regression algorithms are well-suited for these tasks. However, the options are much more limited when the prediction target is multivariate and a joint measure of uncertainty is required. For example, in predicting a 2D velocity vector a joint uncertainty would quantify the probability of any vector in the plane, which would be more expressive than two separate uncertainties on the x- and y- components. To enable joint probabilistic regression, we propose a Natural Gradient Boosting (NGBoost) approach based on nonparametrically modeling the conditional parameters of the multivariate predictive distribution. Our method is robust, works out-of-the-box without extensive tuning, is modular with respect to the assumed target distribution, and performs competitively in comparison to existing approaches. We demonstrate these claims in simulation and with a case study predicting two-dimensional oceanographic velocity data. 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