Non-asymptotic Properties of Generalized Mondrian Forests in Statistical Learning

Random Forests have been extensively used in regression and classification, inspiring the development of various forest-based methods. Among these, Mondrian Forests, derived from the Mondrian process, mark a significant advancement. Expanding on Mondrian Forests, this paper presents a general framework for statistical learning, encompassing a range of common learning tasks such as least squares regression, ${\mathrm{\ell }}_1$ regression, quantile regression, and classification. Under mild assumptions on the loss functions, we provide upper bounds on the regret/risk functions for the estimators and demonstrate their statistical consistency.