Biases in Inverse Ising Estimates of Near-Critical Behaviour

• URL: http://arxiv.org/abs/2301.05556v1
• Date: Fri, 13 Jan 2023 14:01:43 GMT
• Title: Biases in Inverse Ising Estimates of Near-Critical Behaviour
• Authors: Maximilian Benedikt Kloucek, Thomas Machon, Shogo Kajimura, C. Patrick Royall, Naoki Masuda, Francesco Turci
• Abstract summary: Inverse inference allows pairwise interactions to be reconstructed from empirical correlations. We show that estimators used for this inference, such as Pseudo-likelihood (PLM), are biased. Data-driven methods are explored and applied to a functional magnetic resonance imaging (fMRI) dataset from neuroscience.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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