# Learning the Inverse Temperature of Ising Models under Hard Constraints using One Sample

arXiv: https://arxiv.org/abs/2509.20993 · HTML: https://mlsanity.com/paper/2509.20993/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 52 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Builds on (most cited first, 22 of 22)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Efficiently learning Ising models on arbitrary graphs](https://mlsanity.com/paper/1411.6156/) (2014)
- [Efficient Statistics, in High Dimensions, from Truncated Samples](https://mlsanity.com/paper/1809.03986/) (2018)
- [Computationally and Statistically Efficient Truncated Regression](https://mlsanity.com/paper/2010.12000/) (2020)
- [Testing Ising Models](https://mlsanity.com/paper/1612.03147/) (2016)
- [Information Theoretic Properties of Markov Random Fields, and their Algorithmic Applications](https://mlsanity.com/paper/1705.11107/) (2017)
- [Efficient Algorithms for Learning from Coarse Labels](https://mlsanity.com/paper/2108.09805/) (2021)
- [Outlier-Robust Learning of Ising Models Under Dobrushin's Condition](https://mlsanity.com/paper/2102.02171/) (2021)
- [Efficient Parameter Estimation of Truncated Boolean Product Distributions](https://mlsanity.com/paper/2007.02392/) (2020)
- [On the Analysis of EM for truncated mixtures of two Gaussians](https://mlsanity.com/paper/1902.06958/) (2019)
- [Regression from Dependent Observations](https://mlsanity.com/paper/1905.03353/) (2019)
- [Uniform Sampling through the Lov'asz Local Lemma](https://mlsanity.com/paper/1611.01647/) (2016)
- [Learning from Censored and Dependent Data: The case of Linear Dynamics](https://mlsanity.com/paper/2104.05087/) (2021)
- [Statistical Estimation from Dependent Data](https://mlsanity.com/paper/2107.09773/) (2021)
- [Testing Convex Truncation](https://mlsanity.com/paper/2305.03146/) (2023)
- [Learning Hard-Constrained Models with One Sample](https://mlsanity.com/paper/2311.03332/) (2023)
- [Logistic-Regression with peer-group effects via inference in higher order Ising models](https://mlsanity.com/paper/2003.08259/) (2020)
- [Efficient Statistics for Sparse Graphical Models from Truncated Samples](https://mlsanity.com/paper/2006.09735/) (2020)
- [Estimation in Tensor Ising Models](https://mlsanity.com/paper/2008.12882/) (2020)
- [Structure Learning of H-colorings](https://mlsanity.com/paper/1708.05118/) (2017)
- [High Dimensional Logistic Regression Under Network Dependence](https://mlsanity.com/paper/2110.03200/) (2021)

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

- [Efficient Learning of Truncated Boolean Product Distributions: Influence to the Rescue](https://mlsanity.com/paper/2607.22889/) (2026)

## Abstract (arXiv)

We consider the problem of estimating inverse temperature parameter β of an n-dimensional truncated Ising model using a single sample. Given a graph G = (V,E) with n vertices, a truncated Ising model is a probability distribution over the n-dimensional hypercube -1,1n where each configuration σ is constrained to lie in a truncation set S subseteq -1,1n and has probability Pr(σ) propto exp(βσ^top Aσ) with A being the adjacency matrix of G. We adopt the recent setting of [Galanis et al. SODA'24], where the truncation set S can be expressed as the set of satisfying assignments of a k-SAT formula. Given a single sample σ from a truncated Ising model, with inverse parameter β^*, underlying graph G of bounded degree Delta and S being expressed as the set of satisfying assignments of a k-SAT formula, we design in nearly O(n) time an estimator hatβ that is O(Delta3/√n)-consistent with the true parameter β^* for k gtrsim log(d2k)Delta3. Our estimator is based on the maximization of the pseudolikelihood, a notion that has received extensive analysis for various probabilistic models without [Chatterjee, Annals of Statistics '07] or with truncation [Galanis et al. SODA '24]. Our approach generalizes recent techniques from [Daskalakis et al. STOC '19, Galanis et al. SODA '24], to confront the more challenging setting of the truncated Ising model.