Biases in Inverse Ising Estimates of Near-Critical Behaviour

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 model as a benchmark, we show that these biases are large in critical regimes close to phase boundaries, and they 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 data set from neuroscience. Our results indicate that additional care should be taken when attributing criticality to real-world data sets.