Biases in inverse Ising estimates of near-critical behavior

Maximilian B. Kloucek, Thomas Machon, Shogo Kajimura, C. Patrick Royall, Naoki Masuda, Francesco Turci

Research output: Contribution to journalArticle (Academic Journal)peer-review


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.
Original languageEnglish
Article number014109
JournalPhysical Review E
Issue number1
Publication statusPublished - 7 Jul 2023

Bibliographical note

Funding Information:
This work was supported by the EPSRC Centre for Doctoral Training in Functional Materials: The Bristol Centre for Functional Nanomaterials (BCFN) with grant code EP/L016648/1. N.M. acknowledges support from the Japan Science and Technology Agency (JST) Moonshot R&D (under Grant No. JPMJMS2021).

Publisher Copyright:
© 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the ""Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.


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