Notice
Random Tessellation Forests
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Descriptif
Random forests are a popular class of algorithms used for regression and classification. The original algorithm introduced by Breiman in 2001 and many of its variants are ensembles of randomized decision trees built from axis-aligned partitions of the feature space. One such variant, called Mondrian random forests, were proposed to handle the online setting and are the first class of random forests for which minimax rates were obtained in arbitrary dimension. However, the restriction to axis-aligned splits fails to capture dependencies between features, and oblique splits have shown improved empirical performance for many tasks. By viewing the Mondrian as a special case of the stable under iterated (STIT) process in stochastic geometry, we resolve some open questions about the generalization of split directions. In particular, we utilize the theory of stationary random tessellations to show that STIT random forests achieve minimax rates for Lipschitz and C^2 functions. This work opens many new questions at the intersection of stochastic geometry and machine learning. Based on joint work with Ngoc Tran.
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