# Biases in Inverse Ising Estimates of Near-Critical Behaviour

arXiv: https://arxiv.org/abs/2301.05556 · HTML: https://mlsanity.com/paper/2301.05556/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 75 references that are in the map.
- First posted on arXiv 13 Jan 2023.

## Builds on (most cited first, 6 of 6)

- [Inverse statistical problems: from the inverse Ising problem to data science](https://mlsanity.com/paper/1702.01522/) (2017)
- [Optimal structure and parameter learning of Ising models](https://mlsanity.com/paper/1612.05024/) (2016)
- [Searching for collective behavior in a network of real neurons](https://mlsanity.com/paper/1306.3061/) (2013)
- [25 years of criticality in neuroscience -- established results, open controversies, novel concepts](https://mlsanity.com/paper/1903.05129/) (2019)
- [Bias in parametric estimation: reduction and useful side-effects](https://mlsanity.com/paper/1311.6311/) (2013)
- [Universal Organization of Resting Brain Activity at the Thermodynamic Critical Point](https://mlsanity.com/paper/1304.3748/) (2013)

## Built on by (most cited first, 1 of 1)

- [Understanding temperature tuning in energy-based models](https://mlsanity.com/paper/2512.09152/) (2025)

## Abstract (arXiv)

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.