The regression problem of modeling several response variables using the same set of input variables is considered. The model is linearly parameterized and the parameters are estimated by minimizing the error sum of squares subject to a sparsity constraint. The constraint has the effect of eliminating useless inputs and constraining the parameters of the remaining inputs in the model. Two algorithms for solving the resulting convex cone programming problem are proposed. The first algorithm gives a pointwise solution, while the second one computes the entire path of solutions as a function of the constraint parameter. Based on experiments with real data sets, the proposed method has a similar performance to existing methods. In simulation experiments, the proposed method is competitive both in terms of prediction accuracy and correctness of input selection. The advantages become more apparent when many correlated inputs are available for model construction.

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Abstract-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.

Abstract-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.

No abstract