An Empirical Bayes Jackknife Regression Framework for Covariance Matrix Estimation

TL;DR

This paper introduces an empirical Bayes jackknife regression framework for covariance matrix estimation that combines jackknife techniques with machine learning, demonstrating superior performance in simulations and gene network inference.

Contribution

It presents a novel, assumption-free algorithm that frames covariance estimation as a decision problem and integrates jackknife and machine learning methods.

Findings

Outperforms several state-of-the-art methods in simulations

Effective in gene network inference from RNA-seq data

Adapts well across diverse scenarios

Abstract

Covariance matrix estimation, a classical statistical topic, poses significant challenges when the sample size is comparable to or smaller than the number of features. In this paper, we frame covariance matrix estimation as a compound decision problem and apply an optimal decision rule to estimate covariance parameters. To approximate this rule, we introduce an algorithm that integrates jackknife techniques with machine learning regression methods. This algorithm exhibits adaptability across diverse scenarios without relying on assumptions about data distribution. Simulation results and gene network inference from an RNA-seq experiment in mice demonstrate that our approach either matches or surpasses several state-of-the-art methods