Learning Juntas under Markov Random Fields

Gautam Chandrasekaran, Adam Klivans

Keywords: pac learning, learning juntas, smoothed analysis, ising models, markov random fields

TL;DR: We give a polynomial time algorithm for learning $O(log n)$-juntas over smoothed Markov Random fields

Abstract: We give an algorithm for learning $O(\log n)$ juntas in polynomial-time with respect to Markov Random Fields (MRFs) in a smoothed analysis framework, where only the external field has been randomly perturbed. This is a broad generalization of the work of Kalai and Teng, who gave an algorithm that succeeded with respect to smoothed *product* distributions (i.e., MRFs whose dependency graph has no edges). Our algorithm has two phases: (1) an unsupervised structure learning phase and (2) a greedy supervised learning algorithm. This is the first example where algorithms for learning the structure of undirected graphical models have downstream applications to supervised learning.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 22990