Tree-Guided Group Lasso For Multi-Task Regression With Structured Sparsity

Abstract

We consider the problem of learning a sparse multi-task regression,where the structure in the output scan be represented as a tree with leaf nodes as outputs and internal nodes as clusters of the outputs at multiple granularity. Our goal is to recover the common set of relevant inputs for each output cluster. Assuming that the tree structure is available as prior knowledge,we formulate this problem as a new multi-task regularized regression called tree-guided group lasso. Our structured regularization is based on a group-lasso penalty, where groups are defined with respect to the tree structure. We describe a systematic weighting scheme for the groups in the penalty such that each output variable is penalized in a balanced manner even if the groups overlap.We present an efficient optimization method that can handle a large-scale problem. % as is typically the case in association mapping. Using simulated and yeast datasets, we demonstrate that our method shows a superior performance in terms of both prediction error sand recovery of true sparsity patterns compared to other methods for multi-task learning.