# Concentration of Multilinear Functions of the Ising Model with Applications to Network Data

arXiv: https://arxiv.org/abs/1710.04170 · HTML: https://mlsanity.com/paper/1710.04170/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2017.

## Built on by (most cited first, 5 of 5)

- [Outlier-Robust Learning of Ising Models Under Dobrushin's Condition](https://mlsanity.com/paper/2102.02171/) (2021)
- [Statistical Estimation from Dependent Data](https://mlsanity.com/paper/2107.09773/) (2021)
- [Optimal SQ Lower Bounds for Robustly Learning Discrete Product Distributions and Ising Models](https://mlsanity.com/paper/2206.04589/) (2022)
- [Near-Optimal Degree Testing for Bayes Nets](https://mlsanity.com/paper/2304.06733/) (2023)
- [Causal Inference for Sequential Settings under Interference and Latent Confounding](https://mlsanity.com/paper/2607.14940/) (2026)

## Abstract (arXiv)

We prove near-tight concentration of measure for polynomial functions of the Ising model under high temperature. For any degree d, we show that a degree-d polynomial of a n-spin Ising model exhibits exponential tails that scale as exp(-r2/d) at radius r=tildeOmegad(nd/2). Our concentration radius is optimal up to logarithmic factors for constant d, improving known results by polynomial factors in the number of spins. We demonstrate the efficacy of polynomial functions as statistics for testing the strength of interactions in social networks in both synthetic and real world data.