Common Subset Selection of Inputs in Multiresponse Regression

We propose the multiresponse sparse regression algorithm, an input selection method for the purpose of estimating several response variables. It is a forward selection procedure for linearly parameterized models, which updates with carefully chosen step lengths. The step length rule extends the correlation criterion of the least angle regression algorithm for many responses. We present a general concept and explicit formulas for three different variants of the algorithm. Based on experiments with simulated data, the proposed method competes favorably with other methods when many correlated inputs are available for model construction. We also study the performance with several real data sets.