An algorithm for the multivariate group lasso with covariance estimation

TL;DR

This paper introduces a group lasso estimator for multivariate linear regression that accounts for correlated errors, using a block coordinate descent algorithm, with demonstrated effectiveness on simulated and real gene expression data.

Contribution

The paper proposes a novel group lasso estimator tailored for multivariate regression with correlated errors, along with an efficient computational algorithm.

Findings

The estimator performs well in simulation studies with categorical and time series data.

It outperforms alternative estimators in the simulation scenarios.

The method successfully analyzes gene expression time series data.

Abstract

We study a group lasso estimator for the multivariate linear regression model that accounts for correlated error terms. A block coordinate descent algorithm is used to compute this estimator. We perform a simulation study with categorical data and multivariate time series data, typical settings with a natural grouping among the predictor variables. Our simulation studies show the good performance of the proposed group lasso estimator compared to alternative estimators. We illustrate the method on a time series data set of gene expressions.