A Global Homogeneity Test for High-Dimensional Linear Regression

TL;DR

This paper introduces a new statistical test for comparing high-dimensional linear regression models, especially useful for genetic network analysis, controlling errors explicitly and adapting to sparsity.

Contribution

It proposes a novel high-dimensional two-sample test based on multiple testing and variable selection, with explicit error control and minimax adaptivity.

Findings

Test performs well on simulated data.

Effective in high-dimensional settings where p > n.

Applicable to genetic network comparison.

Abstract

This paper is motivated by the comparison of genetic networks based on microarray samples. The aim is to test whether the differences observed between two inferred Gaussian graphical models come from real differences or arise from estimation uncertainties. Adopting a neighborhood approach, we consider a two-sample linear regression model with random design and propose a procedure to test whether these two regressions are the same. Relying on multiple testing and variable selection strategies, we develop a testing procedure that applies to high-dimensional settings where the number of covariates $p$ is larger than the number of observations $n_1$ and $n_2$ of the two samples. Both type I and type II errors are explicitely controlled from a non-asymptotic perspective and the test is proved to be minimax adaptive to the sparsity. The performances of the test are evaluated on simulated data. Moreover, we illustrate how this procedure can be used to compare genetic networks on Hess \emph{et al} breast cancer microarray dataset.