# On approximating the f-divergence between two Ising models

arXiv: https://arxiv.org/abs/2509.05016 · HTML: https://mlsanity.com/paper/2509.05016/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 34 references that are in the map.
- First posted on arXiv 5 Sep 2025.

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

- [Efficiently learning Ising models on arbitrary graphs](https://mlsanity.com/paper/1411.6156/) (2014)
- [Neural Estimation of Statistical Divergences](https://mlsanity.com/paper/2110.03652/) (2021)
- [Practical and Consistent Estimation of f-Divergences](https://mlsanity.com/paper/1905.11112/) (2019)
- [Testing Ising Models](https://mlsanity.com/paper/1612.03147/) (2016)
- [Efficient Distance Approximation for Structured High-Dimensional Distributions via Learning](https://mlsanity.com/paper/2002.05378/) (2020)
- [On Approximating Total Variation Distance](https://mlsanity.com/paper/2206.07209/) (2022)
- [Optimal Mixing of Glauber Dynamics: Entropy Factorization via High-Dimensional Expansion](https://mlsanity.com/paper/2011.02075/) (2020)
- [On Computing the Total Variation Distance of Hidden Markov Models](https://mlsanity.com/paper/1804.06170/) (2018)
- [A simple polynomial-time approximation algorithm for the total variation distance between two product distributions](https://mlsanity.com/paper/2208.00740/) (2022)
- [On Deterministically Approximating Total Variation Distance](https://mlsanity.com/paper/2309.14696/) (2023)
- [Total Variation Distance Meets Probabilistic Inference](https://mlsanity.com/paper/2309.09134/) (2023)
- [Complexity of High-Dimensional Identity Testing with Coordinate Conditional Sampling](https://mlsanity.com/paper/2207.09102/) (2022)
- [Rapid Mixing at the Uniqueness Threshold](https://mlsanity.com/paper/2411.03413/) (2024)
- [Computing Divergences between Discrete Decomposable Models](https://mlsanity.com/paper/2112.04583/) (2021)
- [A Circus of Circuits: Connections Between Decision Diagrams, Circuits, and Automata](https://mlsanity.com/paper/2404.09674/) (2024)
- [Computational Explorations of Total Variation Distance](https://mlsanity.com/paper/2412.10370/) (2024)
- [The Ising Partition Function: Zeros and Deterministic Approximation](https://mlsanity.com/paper/1704.06493/) (2017)
- [Sharp bounds on aggregate expert error](https://mlsanity.com/paper/2407.16642/) (2024)
- [Approximating the total variation distance between spin systems](https://mlsanity.com/paper/2502.05437/) (2025)
- [Algorithms and Hardness for Estimating Statistical Similarity](https://mlsanity.com/paper/2502.10527/) (2025)
- [Approximating the Total Variation Distance between Gaussians](https://mlsanity.com/paper/2503.11099/) (2025)
- [Sampling and Identity-Testing Without Approximate Tensorization of Entropy](https://mlsanity.com/paper/2506.23456/) (2025)

## Abstract (arXiv)

The f-divergence is a fundamental notion that measures the difference between two distributions. In this paper, we study the problem of approximating the f-divergence between two Ising models, which is a generalization of recent work on approximating the TV-distance. Given two Ising models nu and μ, which are specified by their interaction matrices and external fields, the problem is to approximate the f-divergence Df(nu,|,μ) within an arbitrary relative error e± varepsilon. For chiα-divergence with a constant integer α, we establish both algorithmic and hardness results. The algorithm works in a parameter regime that matches the hardness result. Our algorithm can be extended to other f-divergences such as α-divergence, Kullback-Leibler divergence, R'enyi divergence, Jensen-Shannon divergence, and squared Hellinger distance.