Biases in Inverse Ising Estimates of Near-Critical Behaviour

TL;DR

This paper investigates biases in inverse Ising inference, especially near critical points, demonstrating how these biases can mislead interpretations of criticality in complex systems, with implications for neuroscience data analysis.

Contribution

It reveals significant biases in common inference methods near critical regimes and explores bias correction techniques using real neural data.

Findings

Biases are large near phase boundaries in the SK model

PLM inference can falsely suggest criticality in data

Bias correction methods improve inference accuracy

Abstract

Inverse Ising inference allows pairwise interactions of complex binary systems to be reconstructed from empirical correlations. Typical estimators used for this inference, such as Pseudo-likelihood maximization (PLM), are biased. Using the Sherrington-Kirkpatrick (SK) model as a benchmark, we show that these biases are large in critical regimes close to phase boundaries, and may alter the qualitative interpretation of the inferred model. In particular, we show that the small-sample bias causes models inferred through PLM to appear closer-to-criticality than one would expect from the data. Data-driven methods to correct this bias are explored and applied to a functional magnetic resonance imaging (fMRI) dataset from neuroscience. Our results indicate that additional care should be taken when attributing criticality to real-world datasets.