Riemann-Lebesgue Forest for Regression

Tian Qin, Wei-Min Huang

Keywords: RandomForest; Lebesgue Partition; asymptotic normality;

TL;DR: This paper developed a novel tree based ensemble method with the idea of Lebesgue partition.

Abstract:

We propose a novel ensemble method called Riemann-Lebesgue Forest (RLF) for regression. The core idea in RLF is to mimic the way how a measurable function can be approximated by partitioning its range into a few intervals. With this idea in mind, we develop a new tree learner named Riemann-Lebesgue Tree (RLT) which has a chance to perform Lebesgue type cutting,i.e splitting the node from response Y
at certain non-terminal nodes. In other words, we introduce the "splitting type randomness" in our ensemble method. We show that the optimal Lebesgue type cutting results in larger variance reduction in response Y than ordinary CART cutting (an analogue of Riemann partition). Such property is beneficial to the ensemble part of RLF. We also generalize the asymptotic normality of RLF under different parameter settings. Two one-dimensional examples are provided to illustrate the flexibility of RLF. The competitive performance of RLF against original random forest is demonstrated by experiments in simulation data and real world datasets.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 5010