On the Statistical Efficiency of $\ell_{1,p}$ Multi-Task Learning of Gaussian Graphical Models

TL;DR

This paper investigates the statistical efficiency of $,p$ multi-task learning for Gaussian graphical models, providing theoretical bounds and empirical validation on synthetic and real-world data.

Contribution

It introduces $,p$ multi-task structure learning, analyzes sample complexity for support recovery, and compares multi-task with single-task learning.

Findings

Multi-task learning improves support recovery efficiency.

Theoretical bounds on sample size for accurate support detection.

Empirical validation on fMRI and gene expression datasets.

Abstract

In this paper, we present $\ell_{1,p}$ multi-task structure learning for Gaussian graphical models. We analyze the sufficient number of samples for the correct recovery of the support union and edge signs. We also analyze the necessary number of samples for any conceivable method by providing information-theoretic lower bounds. We compare the statistical efficiency of multi-task learning versus that of single-task learning. For experiments, we use a block coordinate descent method that is provably convergent and generates a sequence of positive definite solutions. We provide experimental validation on synthetic data as well as on two publicly available real-world data sets, including functional magnetic resonance imaging and gene expression data.