Transfer Learning in Large-scale Gaussian Graphical Models with False Discovery Rate Control

TL;DR

This paper introduces a transfer learning method for high-dimensional Gaussian graphical models that improves estimation accuracy and controls false discovery rate, demonstrated through simulations and gene network analysis.

Contribution

It proposes Trans-CLIME, a novel transfer learning algorithm with faster convergence, and a debiased estimator for FDR-controlled edge detection in GGMs.

Findings

Faster convergence rate than minimax in single study setting

Element-wise asymptotic normality of the estimator

Improved gene network inference with lower prediction errors

Abstract

Transfer learning for high-dimensional Gaussian graphical models (GGMs) is studied with the goal of estimating the target GGM by utilizing the data from similar and related auxiliary studies. The similarity between the target graph and each auxiliary graph is characterized by the sparsity of a divergence matrix. An estimation algorithm, Trans-CLIME, is proposed and shown to attain a faster convergence rate than the minimax rate in the single study setting. Furthermore, a debiased Trans-CLIME estimator is introduced and shown to be element-wise asymptotically normal. It is used to construct a multiple testing procedure for edge detection with false discovery rate control. The proposed estimation and multiple testing procedures demonstrate superior numerical performance in simulations and are applied to infer the gene networks in a target brain tissue by leveraging the gene expressions from multiple other brain tissues. A significant decrease in prediction errors and a significant increase in power for link detection are observed.