Interaction Screening and Pseudolikelihood Approaches for Tensor Learning in Ising Models

• URL: http://arxiv.org/abs/2310.13232v1
• Date: Fri, 20 Oct 2023 02:42:32 GMT
• Title: Interaction Screening and Pseudolikelihood Approaches for Tensor Learning in Ising Models
• Authors: Tianyu Liu and Somabha Mukherjee
• Abstract summary: We study two well known methods of Ising structure learning, namely the pseudolikelihood approach and the interaction screening approach. We show that both approaches retrieve the underlying hypernetwork structure using a sample size logarithmic in the number of network nodes.
• Score: 8.622642118842624
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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. Finally, we provide a comparative discussion of the performance of the two approaches based on simulation studies, which also demonstrate the exponential dependence of the tensor recovery rate on the maximum coupling strength.

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