Optimal structure and parameter learning of Ising models

TL;DR

This paper introduces Interaction Screening, a new efficient method for accurately reconstructing the structure and parameters of Ising models from data, achieving optimal sample complexity even in challenging regimes.

Contribution

The paper presents a novel local optimization-based algorithm, Interaction Screening, that guarantees perfect graph recovery with minimal data, improving upon existing methods in the inverse Ising problem.

Findings

Achieves perfect graph recovery with optimal sample complexity.

Performs well on synthetic and real data, including quantum computer outputs.

Proven to be an exact and tractable solution for the inverse Ising problem.

Abstract

Reconstruction of structure and parameters of an Ising model from binary samples is a problem of practical importance in a variety of disciplines, ranging from statistical physics and computational biology to image processing and machine learning. The focus of the research community shifted towards developing universal reconstruction algorithms which are both computationally efficient and require the minimal amount of expensive data. We introduce a new method, Interaction Screening, which accurately estimates the model parameters using local optimization problems. The algorithm provably achieves perfect graph structure recovery with an information-theoretically optimal number of samples, notably in the low-temperature regime which is known to be the hardest for learning. The efficacy of Interaction Screening is assessed through extensive numerical tests on synthetic Ising models of various topologies with different types of interactions, as well as on a real data produced by a D-Wave quantum computer. This study shows that the Interaction Screening method is an exact, tractable and optimal technique universally solving the inverse Ising problem.