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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2202.05612 |
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| _version_ | 1866913201144201216 |
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| author | Wei, Haoyu Lei, Xiaoyu Han, Yixin Zhang, Huiming |
| author_facet | Wei, Haoyu Lei, Xiaoyu Han, Yixin Zhang, Huiming |
| contents | Identifying important features linked to a response variable is a fundamental task in various scientific domains. This article explores statistical inference for simulated Markov random fields in high-dimensional settings. We introduce a methodology based on Markov Chain Monte Carlo Maximum Likelihood Estimation (MCMC-MLE) with Elastic-net regularization. Under mild conditions on the MCMC method, our penalized MCMC-MLE method achieves $\ell_{1}$-consistency. We propose a decorrelated score test, establishing both its asymptotic normality and that of a one-step estimator, along with the associated confidence interval. Furthermore, we construct two false discovery rate control procedures via the asymptotic behaviors for both p-values and e-values. Comprehensive numerical simulations confirm the theoretical validity of the proposed methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_05612 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | High-dimensional Inference and FDR Control for Simulated Markov Random Fields Wei, Haoyu Lei, Xiaoyu Han, Yixin Zhang, Huiming Machine Learning Statistics Theory Identifying important features linked to a response variable is a fundamental task in various scientific domains. This article explores statistical inference for simulated Markov random fields in high-dimensional settings. We introduce a methodology based on Markov Chain Monte Carlo Maximum Likelihood Estimation (MCMC-MLE) with Elastic-net regularization. Under mild conditions on the MCMC method, our penalized MCMC-MLE method achieves $\ell_{1}$-consistency. We propose a decorrelated score test, establishing both its asymptotic normality and that of a one-step estimator, along with the associated confidence interval. Furthermore, we construct two false discovery rate control procedures via the asymptotic behaviors for both p-values and e-values. Comprehensive numerical simulations confirm the theoretical validity of the proposed methods. |
| title | High-dimensional Inference and FDR Control for Simulated Markov Random Fields |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2202.05612 |