Adaptive Cluster Expansion for Inferring Boltzmann Machines with Noisy Data

TL;DR

This paper presents an adaptive cluster expansion method for inferring Boltzmann (Ising) models from noisy data, effectively identifying interactions among binary variables and robustly handling sampling noise.

Contribution

It introduces a novel cluster expansion algorithm that accurately infers interactions in Ising models even with noisy data and critical phenomena.

Findings

Successfully recovers benchmark Ising models at criticality

Effective in low-temperature phases

Applied to neurobiological data

Abstract

We introduce a procedure to infer the interactions among a set of binary variables, based on their sampled frequencies and pairwise correlations. The algorithm builds the clusters of variables contributing most to the entropy of the inferred Ising model, and rejects the small contributions due to the sampling noise. Our procedure successfully recovers benchmark Ising models even at criticality and in the low temperature phase, and is applied to neurobiological data.