Interaction Screening and Pseudolikelihood Approaches for Tensor Learning in Ising Models
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916339958939648 |
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| author | Liu, Tianyu Mukherjee, Somabha |
| author_facet | Liu, Tianyu Mukherjee, Somabha |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13232 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Interaction Screening and Pseudolikelihood Approaches for Tensor Learning in Ising Models Liu, Tianyu Mukherjee, Somabha Methodology Statistics Theory Machine Learning 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. |
| title | Interaction Screening and Pseudolikelihood Approaches for Tensor Learning in Ising Models |
| topic | Methodology Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2310.13232 |