Agnostically Learning Juntas from Random Walks

TL;DR

This paper presents a polynomial-time algorithm for agnostically learning k-juntas from random walks, even when the target function is arbitrary, extending the understanding of learning theory in complex, high-dimensional settings.

Contribution

It introduces the first polynomial-time agnostic learning algorithm for k-juntas from random walks, with explicit complexity bounds depending on k, epsilon, and delta.

Findings

Algorithm successfully learns k-juntas from random walks.

Provides bounds on running time based on parameters n, k, epsilon, delta.

Achieves near-optimal approximation to the target function.

Abstract

We prove that the class of functions g:{-1,+1}^n -> {-1,+1} that only depend on an unknown subset of k<<n variables (so-called k-juntas) is agnostically learnable from a random walk in time polynomial in n, 2^{k^2}, epsilon^{-k}, and log(1/delta). In other words, there is an algorithm with the claimed running time that, given epsilon, delta > 0 and access to a random walk on {-1,+1}^n labeled by an arbitrary function f:{-1,+1}^n -> {-1,+1}, finds with probability at least 1-delta a k-junta that is (opt(f)+epsilon)-close to f, where opt(f) denotes the distance of a closest k-junta to f.