Interaction Screening: Efficient and Sample-Optimal Learning of Ising Models

TL;DR

This paper introduces an interaction screening method for efficiently learning the structure of Ising models from samples, achieving near-optimal sample complexity with a convex optimization approach.

Contribution

It proposes a new, computationally efficient estimator with physical interpretation that recovers the underlying graph with near-optimal sample complexity.

Findings

Estimator is consistent and efficiently implemented.

Sample complexity is logarithmic in system size p.

Sample complexity is exponential in maximum coupling and degree.

Abstract

We consider the problem of learning the underlying graph of an unknown Ising model on p spins from a collection of i.i.d. samples generated from the model. We suggest a new estimator that is computationally efficient and requires a number of samples that is near-optimal with respect to previously established information-theoretic lower-bound. Our statistical estimator has a physical interpretation in terms of "interaction screening". The estimator is consistent and is efficiently implemented using convex optimization. We prove that with appropriate regularization, the estimator recovers the underlying graph using a number of samples that is logarithmic in the system size p and exponential in the maximum coupling-intensity and maximum node-degree.