High-dimensional Inference and FDR Control for Simulated Markov Random Fields

TL;DR

This work addresses high-dimensional inference for Markov Random Fields modeled as canonical exponential families with intractable normalizing constants. It develops a penalized MCMC-MLE approach using Elastic-net regularization to achieve $\ell_1$-consistency, and introduces a decorrelated score test with a one-step estimator that is asymptotically normal, enabling confidence intervals for a targeted parameter. The paper also proposes two FDR control procedures, one based on p-values (via data splitting) and one based on e-values, and demonstrates their validity through rigorous theory and simulations. Together, these methods enable reliable structure-agnostic inference in large graphical models and offer practical tools for detecting important features while controlling false discoveries in high dimensions.

Abstract

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.

Figures (1)

• Figure 1: Empirical rejection rate under $N = 100$ replications.

Theorems & Definitions (30)

• Lemma 3.1
• Lemma 3.2
• Theorem 3.1
• Lemma 3.3
• Theorem 3.2
• Theorem 4.1
• Theorem 4.2
• Theorem 4.3
• Lemma A.1: Theorem 1 in jiang2018bernstein
• Lemma B.1