Tree-guided group lasso for multi-response regression with structured sparsity, with an application to eQTL mapping

TL;DR

This paper introduces a tree-guided group lasso method for multi-response regression that captures hierarchical response structures, improving prediction accuracy and sparsity pattern recovery in applications like eQTL mapping.

Contribution

The paper proposes a novel tree-guided group lasso with a balanced penalty scheme and an efficient optimization algorithm for structured sparsity in multi-response regression.

Findings

Outperforms existing methods in prediction accuracy.

Effectively recovers true sparsity patterns.

Demonstrated on simulated and yeast eQTL data.

Abstract

We consider the problem of estimating a sparse multi-response regression function, with an application to expression quantitative trait locus (eQTL) mapping, where the goal is to discover genetic variations that influence gene-expression levels. In particular, we investigate a shrinkage technique capable of capturing a given hierarchical structure over the responses, such as a hierarchical clustering tree with leaf nodes for responses and internal nodes for clusters of related responses at multiple granularity, and we seek to leverage this structure to recover covariates relevant to each hierarchically-defined cluster of responses. We propose a tree-guided group lasso, or tree lasso, for estimating such structured sparsity under multi-response regression by employing a novel penalty function constructed from the tree. We describe a systematic weighting scheme for the overlapping groups in the tree-penalty such that each regression coefficient is penalized in a balanced manner despite the inhomogeneous multiplicity of group memberships of the regression coefficients due to overlaps among groups. For efficient optimization, we employ a smoothing proximal gradient method that was originally developed for a general class of structured-sparsity-inducing penalties. Using simulated and yeast data sets, we demonstrate that our method shows a superior performance in terms of both prediction errors and recovery of true sparsity patterns, compared to other methods for learning a multivariate-response regression.