Union Support Recovery in Multi-task Learning

TL;DR

This paper analyzes the effectiveness of various penalization methods for variable selection in multi-task learning, using the Normal means model to simplify and clarify the theoretical understanding of support recovery.

Contribution

It provides a clear characterization of support recovery performance in multi-task learning through the Normal means model, simplifying previous complex analyses.

Findings

Different penalization schemes have distinct support recovery capabilities.

The Normal means model offers a simplified framework for theoretical analysis.

Results clarify conditions under which variable selection is successful.

Abstract

We sharply characterize the performance of different penalization schemes for the problem of selecting the relevant variables in the multi-task setting. Previous work focuses on the regression problem where conditions on the design matrix complicate the analysis. A clearer and simpler picture emerges by studying the Normal means model. This model, often used in the field of statistics, is a simplified model that provides a laboratory for studying complex procedures.