1. Biases in Inverse Ising Estimates of Near-Critical Behaviour
- Author
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Kloucek, Maximilian Benedikt, Machon, Thomas, Kajimura, Shogo, Royall, C. Patrick, Masuda, Naoki, and Turci, Francesco
- Subjects
Condensed Matter - Disordered Systems and Neural Networks ,Condensed Matter - Statistical Mechanics ,Computer Science - Machine Learning - 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.
- Published
- 2023
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