Eliza O’Reilly: Random tessellation forests: overcoming the curse of dimensionality скачать в хорошем качестве

Eliza O’Reilly: Random tessellation forests: overcoming the curse of dimensionality

Random forests are a popular class of algorithms used for regression and classication that are ensembles of randomized decision trees built from axis-aligned partitions of the feature space. However, the restriction to axis-aligned splits fails to capture dependencies between features, and random forest algorithms using oblique splits have shown improved empirical performance. To help explain the advantage of partitioning the data with oblique splits, we consider the class of random tessellations forests, generated by the stable under iteration (STIT) process in stochastic geometry, which achieve minimax optimal convergence rates for Lipschitz and C2 functions for any fixed choice of directional distribution. In this work, we expand on the connection between the theory of stationary random tessellations and statistical learning theory to illustrate how the curse of dimensionality present in these convergence rates can be overcome in high dimensional feature space with a good choice of directional distribution for the random tessellation forest estimator.