# Tensor Recovery in High-Dimensional Ising Models

arXiv: https://arxiv.org/abs/2304.00530 · HTML: https://mlsanity.com/paper/2304.00530/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2023.

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

- [Interaction Screening and Pseudolikelihood Approaches for Tensor Learning in Ising Models](https://mlsanity.com/paper/2310.13232/) (2023)

## Abstract (arXiv)

The k-tensor Ising model is an exponential family on a p-dimensional binary hypercube for modeling dependent binary data, where the sufficient statistic consists of all k-fold products of the observations, and the parameter is an unknown k-fold tensor, designed to capture higher-order interactions between the binary variables. In this paper, we describe an approach based on a penalization technique that helps us recover the signed support of the tensor parameter with high probability, assuming that no entry of the true tensor is too close to zero. The method is based on an ℓ1-regularized node-wise logistic regression, that recovers the signed neighborhood of each node with high probability. Our analysis is carried out in the high-dimensional regime, that allows the dimension p of the Ising model, as well as the interaction factor k to potentially grow to ∞ with the sample size n. We show that if the minimum interaction strength is not too small, then consistent recovery of the entire signed support is possible if one takes n = Omega((k!)8 d3 log binomp-1k-1) samples, where d denotes the maximum degree of the hypernetwork in question. Our results are validated in two simulation settings, and applied on a real neurobiological dataset consisting of multi-array electro-physiological recordings from the mouse visual cortex, to model higher-order interactions between the brain regions.