Eliza O'Reilly: The stochastic geometry of decision tree learning

Title: The stochastic geometry of decision tree learning

 

Affiliation: Applied Mathematics and Statistics, Johns Hopkins University
 

Abstract: Random forests are a widely used class of prediction algorithms made of ensembles of randomized decision trees. The most commonly used algorithms use only one covariate of the input data to partition the data in a given node of a tree. Oblique random forests are variants where splits are allowed to depend on linear combinations of the covariates. In this talk, we will discuss a class of efficiently generated random tree and forest estimators called oblique Mondrian trees and forests, as the trees are generated by first selecting a set of features from linear combinations of the covariates and then running the stochastic Mondrian process that hierarchically partitions the data along these features. Our theoretical analysis illuminates when these estimators can adapt to dimension reduction models for which the output depends on a general low-dimensional relevant feature subspace and we quantify how robust the risk is with respect to error in the estimation of these relevant features. We will then discuss an approach for identifying the relevant feature subspace that uses a Mondrian forest to estimate the expected gradient outer product (EGOP). In addition, we introduce an iterative algorithm called Transformed Iterative Mondrian (TrIM) forest to improve the Mondrian forest estimator by incorporating data-adaptivity in the partitioning process via the EGOP.

 

Bio: Eliza O’Reilly is an assistant professor in the Department of Applied Mathematics and Statistics at Johns Hopkins University. Her research focuses on the development and analysis of new geometric models and algorithms for complex data analysis using point processes, stochastic geometry, and convex geometry. She received her PhD in mathematics from the University of Texas at Austin and was a postdoctoral scholar at the California Institute of Technology before joining JHU.