A Minimum Description Length Approach to Multitask Feature Selection

TL;DR

This paper introduces a novel MDL-based method called MIC for multitask feature selection, effectively sharing information across responses to improve prediction accuracy and hypothesis testing in multi-response regression problems.

Contribution

It extends MDL feature selection to multitask settings with the MIC approach, enhancing feature sharing and improving prediction and testing performance.

Findings

MIC reduces prediction error on synthetic and biological data.

MIC outperforms standard methods in identifying true positives.

The approach effectively shares features across multiple responses.

Abstract

Many regression problems involve not one but several response variables (y's). Often the responses are suspected to share a common underlying structure, in which case it may be advantageous to share information across them; this is known as multitask learning. As a special case, we can use multiple responses to better identify shared predictive features -- a project we might call multitask feature selection. This thesis is organized as follows. Section 1 introduces feature selection for regression, focusing on ell_0 regularization methods and their interpretation within a Minimum Description Length (MDL) framework. Section 2 proposes a novel extension of MDL feature selection to the multitask setting. The approach, called the "Multiple Inclusion Criterion" (MIC), is designed to borrow information across regression tasks by more easily selecting features that are associated with multiple responses. We show in experiments on synthetic and real biological data sets that MIC can reduce prediction error in settings where features are at least partially shared across responses. Section 3 surveys hypothesis testing by regression with a single response, focusing on the parallel between the standard Bonferroni correction and an MDL approach. Mirroring the ideas in Section 2, Section 4 proposes a novel MIC approach to hypothesis testing with multiple responses and shows that on synthetic data with significant sharing of features across responses, MIC sometimes outperforms standard FDR-controlling methods in terms of finding true positives for a given level of false positives. Section 5 concludes.