CO2 Forest: Improved Random Forest by Continuous Optimization of Oblique Splits

TL;DR

This paper introduces CO2 Forest, an improved random forest method that optimizes oblique splits via continuous convex optimization, leading to better classification performance on benchmarks.

Contribution

It presents a novel convex optimization approach for oblique split functions in decision trees, outperforming traditional univariate split methods and prior oblique tree techniques.

Findings

Significantly outperforms standard Random Forests with univariate splits.

Achieves superior accuracy on multi-class benchmarks.

Demonstrates effectiveness on Labeled Faces in the Wild dataset.

Abstract

We propose a novel algorithm for optimizing multivariate linear threshold functions as split functions of decision trees to create improved Random Forest classifiers. Standard tree induction methods resort to sampling and exhaustive search to find good univariate split functions. In contrast, our method computes a linear combination of the features at each node, and optimizes the parameters of the linear combination (oblique) split functions by adopting a variant of latent variable SVM formulation. We develop a convex-concave upper bound on the classification loss for a one-level decision tree, and optimize the bound by stochastic gradient descent at each internal node of the tree. Forests of up to 1000 Continuously Optimized Oblique (CO2) decision trees are created, which significantly outperform Random Forest with univariate splits and previous techniques for constructing oblique trees. Experimental results are reported on multi-class classification benchmarks and on Labeled Faces in the Wild (LFW) dataset.