Learning Ising Models with Independent Failures

TL;DR

This paper introduces an efficient algorithm for learning the structure of Ising models even when data entries are missing independently, matching optimal bounds in runtime and sample complexity.

Contribution

It presents the first efficient method to learn Ising models with independent missing data, using a novel unbiased gradient estimator and stochastic gradient descent.

Findings

Algorithm achieves optimal runtime and sample complexity.

Successfully recovers neighborhood structure of Ising models.

Handles missing data with unknown probability p.

Abstract

We give the first efficient algorithm for learning the structure of an Ising model that tolerates independent failures; that is, each entry of the observed sample is missing with some unknown probability p. Our algorithm matches the essentially optimal runtime and sample complexity bounds of recent work for learning Ising models due to Klivans and Meka (2017). We devise a novel unbiased estimator for the gradient of the Interaction Screening Objective (ISO) due to Vuffray et al. (2016) and apply a stochastic multiplicative gradient descent algorithm to minimize this objective. Solutions to this minimization recover the neighborhood information of the underlying Ising model on a node by node basis.