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Many regression problems involve not one but several response variables(y's). Often the responses are suspected to share a common underlyingstructure, in which case it may be advantageous to share information acrossthem; this is known as multitask learning. As a special case, we can usemultiple responses to better identify shared predictive features -- a projectwe might call multitask feature selection.  This thesis is organized as follows. Section 1 introduces feature selectionfor regression, focusing on ell_0 regularization methods and theirinterpretation within a Minimum Description Length (MDL) framework. Section 2proposes a novel extension of MDL feature selection to the multitask setting.The approach, called the "Multiple Inclusion Criterion" (MIC), is designed toborrow information across regression tasks by more easily selecting featuresthat are associated with multiple responses. We show in experiments onsynthetic and real biological data sets that MIC can reduce prediction error insettings where features are at least partially shared across responses. Section3 surveys hypothesis testing by regression with a single response, focusing onthe parallel between the standard Bonferroni correction and an MDL approach.Mirroring the ideas in Section 2, Section 4 proposes a novel MIC approach tohypothesis testing with multiple responses and shows that on synthetic datawith significant sharing of features across responses, MIC sometimesoutperforms standard FDR-controlling methods in terms of finding true positivesfor a given level of false positives. Section 5 concludes.

A Minimum Description Length Approach to Multitask Feature Selection