Learning stochastic decision trees

TL;DR

This paper presents a quasipolynomial-time algorithm for learning stochastic decision trees that is optimally resilient to adversarial noise, achieving near-optimal error bounds and producing decision tree hypotheses.

Contribution

It introduces the first proper, noise-resilient learning algorithm for stochastic decision trees with optimal error guarantees.

Findings

Algorithm runs in quasipolynomial time with noise resilience.

Achieves error within 2η + ε of the Bayes optimal.

First proper learning algorithm for stochastic decision trees.

Abstract

We give a quasipolynomial-time algorithm for learning stochastic decision trees that is optimally resilient to adversarial noise. Given an $\eta$-corrupted set of uniform random samples labeled by a size-$s$ stochastic decision tree, our algorithm runs in time $n^{O(\log(s/\varepsilon)/\varepsilon^2)}$ and returns a hypothesis with error within an additive $2\eta + \varepsilon$ of the Bayes optimal. An additive $2\eta$ is the information-theoretic minimum. Previously no non-trivial algorithm with a guarantee of $O(\eta) + \varepsilon$ was known, even for weaker noise models. Our algorithm is furthermore proper, returning a hypothesis that is itself a decision tree; previously no such algorithm was known even in the noiseless setting.