# Interaction Screening and Pseudolikelihood Approaches for Tensor Learning in Ising Models

arXiv: https://arxiv.org/abs/2310.13232 · HTML: https://mlsanity.com/paper/2310.13232/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 39 references that are in the map.
- First posted on arXiv 20 Oct 2023.

## Builds on (most cited first, 12 of 12)

- [Efficiently learning Ising models on arbitrary graphs](https://mlsanity.com/paper/1411.6156/) (2014)
- [Interaction Screening: Efficient and Sample-Optimal Learning of Ising Models](https://mlsanity.com/paper/1605.07252/) (2016)
- [Optimal structure and parameter learning of Ising models](https://mlsanity.com/paper/1612.05024/) (2016)
- [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)
- [Learning a Tree-Structured Ising Model in Order to Make Predictions](https://mlsanity.com/paper/1604.06749/) (2016)
- [The Minimax Learning Rates of Normal and Ising Undirected Graphical Models](https://mlsanity.com/paper/1806.06887/) (2018)
- [Structure learning of antiferromagnetic Ising models](https://mlsanity.com/paper/1412.1443/) (2014)
- [Estimation in Tensor Ising Models](https://mlsanity.com/paper/2008.12882/) (2020)
- [Property Testing in High Dimensional Ising models](https://mlsanity.com/paper/1709.06688/) (2017)
- [High-Temperature Structure Detection in Ferromagnets](https://mlsanity.com/paper/1809.08204/) (2018)
- [Tensor Recovery in High-Dimensional Ising Models](https://mlsanity.com/paper/2304.00530/) (2023)

## Abstract (arXiv)

In this paper, we study two well known methods of Ising structure learning, namely the pseudolikelihood approach and the interaction screening approach, in the context of tensor recovery in k-spin Ising models. We show that both these approaches, with proper regularization, retrieve the underlying hypernetwork structure using a sample size logarithmic in the number of network nodes, and exponential in the maximum interaction strength and maximum node-degree. We also track down the exact dependence of the rate of tensor recovery on the interaction order k, that is allowed to grow with the number of samples and nodes, for both the approaches. We then provide a comparative discussion of the performance of the two approaches based on simulation studies, which also demonstrates the exponential dependence of the tensor recovery rate on the maximum coupling strength. Our tensor recovery methods are then applied on gene data taken from the Curated Microarray Database (CuMiDa), where we focus on understanding the important genes related to hepatocellular carcinoma.