# Optimal structure and parameter learning of Ising models

arXiv: https://arxiv.org/abs/1612.05024 · HTML: https://mlsanity.com/paper/1612.05024/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2016.

## Built on by (most cited first, 26 of 26)

- [Statistical Efficiency of Score Matching: The View from Isoperimetry](https://mlsanity.com/paper/2210.00726/) (2022)
- [Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential families](https://mlsanity.com/paper/2110.04719/) (2021)
- [High-quality Thermal Gibbs Sampling with Quantum Annealing Hardware](https://mlsanity.com/paper/2109.01690/) (2021)
- [Learning Continuous Exponential Families Beyond Gaussian](https://mlsanity.com/paper/2102.09198/) (2021)
- [Exponential Reduction in Sample Complexity with Learning of Ising Model Dynamics](https://mlsanity.com/paper/2104.00995/) (2021)
- [Network reconstruction via the minimum description length principle](https://mlsanity.com/paper/2405.01015/) (2024)
- [Ising Model Selection Using ℓ1-Regularized Linear Regression: A Statistical Mechanics Analysis](https://mlsanity.com/paper/2102.03988/) (2021)
- [Quantum Model Learning Agent: characterisation of quantum systems through machine learning](https://mlsanity.com/paper/2112.08409/) (2021)
- [Learning Gaussian DAG Models without Condition Number Bounds](https://mlsanity.com/paper/2511.06164/) (2025)
- [Estimating Ising Models in Total Variation Distance](https://mlsanity.com/paper/2511.21008/) (2025)
- [Learning Energy-Based Representations of Quantum Many-Body States](https://mlsanity.com/paper/2304.04058/) (2023)
- [Discrete distributions are learnable from metastable samples](https://mlsanity.com/paper/2410.13800/) (2024)
- [A Blueprint for Equilibrium-Based Differentiable Continuous-Variable Thermodynamic Computing](https://mlsanity.com/paper/2607.16183/) (2026)
- [Single-Qubit Fidelity Assessment of Quantum Annealing Hardware](https://mlsanity.com/paper/2104.03335/) (2021)
- [On Model Selection Consistency of Lasso for High-Dimensional Ising Models](https://mlsanity.com/paper/2110.08500/) (2021)
- [Biases in Inverse Ising Estimates of Near-Critical Behaviour](https://mlsanity.com/paper/2301.05556/) (2023)
- [Inference of stochastic time series with missing data](https://mlsanity.com/paper/2101.11816/) (2021)
- [Data-Driven Interaction Analysis of Line Failure Cascading in Power Grid Networks](https://mlsanity.com/paper/2112.01061/) (2021)
- [Interaction Screening and Pseudolikelihood Approaches for Tensor Learning in Ising Models](https://mlsanity.com/paper/2310.13232/) (2023)
- [Mixing Artificial and Natural Intelligence: From Statistical Mechanics to AI and Back to Turbulence](https://mlsanity.com/paper/2403.17993/) (2024)
- [Sparsity-Constraint Optimization via Splicing Iteration](https://mlsanity.com/paper/2406.12017/) (2024)
- [Data augmentation using diffusion models to enhance inverse Ising inference](https://mlsanity.com/paper/2503.10154/) (2025)
- [Efficient Learning of Lattice Gauge Theories with Fermions](https://mlsanity.com/paper/2512.19891/) (2025)
- [Computationally sufficient statistics for Ising models](https://mlsanity.com/paper/2602.12449/) (2026)
- [Selecting Optimal Variable Order in Autoregressive Ising Models](https://mlsanity.com/paper/2602.20394/) (2026)
- [Transfer Learning in High-dimensional Ising Models](https://mlsanity.com/paper/2607.03005/) (2026)

## Abstract (arXiv)

Reconstruction of structure and parameters of an Ising model from binary samples is a problem of practical importance in a variety of disciplines, ranging from statistical physics and computational biology to image processing and machine learning. The focus of the research community shifted towards developing universal reconstruction algorithms which are both computationally efficient and require the minimal amount of expensive data. We introduce a new method, Interaction Screening, which accurately estimates the model parameters using local optimization problems. The algorithm provably achieves perfect graph structure recovery with an information-theoretically optimal number of samples, notably in the low-temperature regime which is known to be the hardest for learning. The efficacy of Interaction Screening is assessed through extensive numerical tests on synthetic Ising models of various topologies with different types of interactions, as well as on a real data produced by a D-Wave quantum computer. This study shows that the Interaction Screening method is an exact, tractable and optimal technique universally solving the inverse Ising problem.