Convex Feature Learning for Multiple Targets via Output Structure Information

Abstract

Multi-target regression has gained popularity owing to its ability to predict multiple outcomes simultaneously, with improved performance over single-target methods. Unlike traditional single-response prediction, multi-target regression faces the additional complexity of managing interdependencies among target variables, which in turn accounts for the relationship between all targets and input-output. In this study, we devised a linear convex multi-target regression (LC-MTR) that simultaneously models and learns the linear convex feature of the output structure that establishes predictor-response and, inter-target correlations. The LC-MTR is designed to capture both the correlations and input-output dependencies among the targets. A novel multi-target optimization technique for large and sparse matrices leverages singular value decomposition (SVD) with the Schur complement, which reduces the computational time associated with estimating weighted regression coefficients in multi-target settings. This optimization technique significantly enhances the training and test performance by ensuring that the learned models are better at capturing complex interlying target patterns. Empirical evaluations demonstrate that LC-MTR outperforms with existing regression methodologies on various real time datasets.

Keywords

• Convex formulation
• inter-target correlations
• linear structure learning
• multi-target regression
• sparse matrices
• optimization