# Computationally sufficient statistics for Ising models

arXiv: https://arxiv.org/abs/2602.12449 · HTML: https://mlsanity.com/paper/2602.12449/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [Efficiently learning Ising models on arbitrary graphs](https://mlsanity.com/paper/1411.6156/) (2014)
- [Interaction Screening: Efficient and Sample-Optimal Learning of Ising Models](https://mlsanity.com/paper/1605.07252/) (2016)
- [Learning Graphical Models Using Multiplicative Weights](https://mlsanity.com/paper/1706.06274/) (2017)
- [Inverse statistical problems: from the inverse Ising problem to data science](https://mlsanity.com/paper/1702.01522/) (2017)
- [A General Characterization of the Statistical Query Complexity](https://mlsanity.com/paper/1608.02198/) (2016)
- [Optimal structure and parameter learning of Ising models](https://mlsanity.com/paper/1612.05024/) (2016)
- [Learning quantum Hamiltonians at any temperature in polynomial time](https://mlsanity.com/paper/2310.02243/) (2023)
- [Efficient Learning of Discrete Graphical Models](https://mlsanity.com/paper/1902.00600/) (2019)
- [Computational Complexity of Statistics: New Insights from Low-Degree Polynomials](https://mlsanity.com/paper/2506.10748/) (2025)
- [Provable benefits of score matching](https://mlsanity.com/paper/2306.01993/) (2023)
- [A Unified Approach to Learning Ising Models: Beyond Independence and Bounded Width](https://mlsanity.com/paper/2311.09197/) (2023)
- [Computational Implications of Reducing Data to Sufficient Statistics](https://mlsanity.com/paper/1409.3821/) (2014)
- [Hardness of parameter estimation in graphical models](https://mlsanity.com/paper/1409.3836/) (2014)
- [Improved algorithms for learning quantum Hamiltonians, via flat polynomials](https://mlsanity.com/paper/2407.04540/) (2024)
- [Discrete distributions are learnable from metastable samples](https://mlsanity.com/paper/2410.13800/) (2024)

## Abstract (arXiv)

Learning Gibbs distributions using only sufficient statistics has long been recognized as a computationally hard problem. On the other hand, computationally efficient algorithms for learning Gibbs distributions rely on access to full sample configurations generated from the model. For many systems of interest that arise in physical contexts, expecting a full sample to be observed is not practical, and hence it is important to look for computationally efficient methods that solve the learning problem with access to only a limited set of statistics. We examine the trade-offs between the power of computation and observation within this scenario, employing the Ising model as a paradigmatic example. We demonstrate that it is feasible to reconstruct the model parameters for a model with ℓ1 width γ by observing statistics up to an order of O(γ). This approach allows us to infer the model's structure and also learn its couplings and magnetic fields. We also discuss a setting where prior information about structure of the model is available and show that the learning problem can be solved efficiently with even more limited observational power.