  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.
