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

arXiv: https://arxiv.org/abs/2202.05612 · HTML: https://mlsanity.com/paper/2202.05612/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 72 references that are in the map.
- First posted on arXiv 11 Feb 2022.

## Builds on (most cited first, 14 of 14)

- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [Deep Knockoffs](https://mlsanity.com/paper/1811.06687/) (2018)
- [A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional Models](https://mlsanity.com/paper/1412.8765/) (2014)
- [Concentration Inequalities for Statistical Inference](https://mlsanity.com/paper/2011.02258/) (2020)
- [False Discovery Rate Control via Data Splitting](https://mlsanity.com/paper/2002.08542/) (2020)
- [Elastic-net Regularized High-dimensional Negative Binomial Regression: Consistency and Weak Signals Detection](https://mlsanity.com/paper/1712.03412/) (2017)
- [A Scale-free Approach for False Discovery Rate Control in Generalized Linear Models](https://mlsanity.com/paper/2007.01237/) (2020)
- [Inference for Individual Mediation Effects and Interventional Effects in Sparse High-Dimensional Causal Graphical Models](https://mlsanity.com/paper/1809.10652/) (2018)
- [Testing and Confidence Intervals for High Dimensional Proportional Hazards Model](https://mlsanity.com/paper/1412.5158/) (2014)
- [Stochastic Learning for Sparse Discrete Markov Random Fields with Controlled Gradient Approximation Error](https://mlsanity.com/paper/2005.06083/) (2020)
- [Sparse estimation in Ising Model via penalized Monte Carlo methods](https://mlsanity.com/paper/1612.07497/) (2016)
- [Relaxing the Assumptions of Knockoffs by Conditioning](https://mlsanity.com/paper/1903.02806/) (2019)
- [False Discovery Rate Control Under General Dependence By Symmetrized Data Aggregation](https://mlsanity.com/paper/2002.11992/) (2020)
- [Directional FDR Control for Sub-Gaussian Sparse GLMs](https://mlsanity.com/paper/2105.00393/) (2021)

## Abstract (arXiv)

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 ℓ1-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.