High-dimensional Inference and FDR Control for Simulated Markov Random Fields
This work addresses feature selection and inference challenges in high-dimensional data for scientific domains, presenting incremental improvements to existing methods.
The paper tackles statistical inference for simulated Markov random fields in high-dimensional settings by introducing a penalized MCMC-MLE method with Elastic-net regularization, achieving ℓ₁-consistency and proposing decorrelated score tests with asymptotic normality and false discovery rate control procedures, with numerical simulations confirming theoretical validity.
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.