Nonparametric multi-task regression under group sparsity and low-rank structures

초록

Regression models find extensive applications across various domains. When multiple output variables are involved, they constitute a multivariate regression model. The objective of such models is to estimate regression functions for each output variable. Classical approaches, such as least squares or maximum likelihood methods, treat each function independently, leading to challenges with parameter estimation as the number of functions increases. Multi-task learning emerges as an alternative approach by leveraging information across related tasks. Reduced-rank regression, which aligns with the multi-task learning idea, addresses this challenge by imposing low-rank constraints on the coefficient matrix to incorporate the low-dimensional structure in the estimation process. The group lasso approach, on the other hand, extends the concept of sparsity-inducing penalization to select important variable subsets. Combining group sparsity and low-rank regularization approaches is expected to offer promising possibilities in multi-task regression. However, no work has explored their combined application within the nonparametric regression framework. In this study, we propose a nonparametric multi-task regression estimator that jointly incorporates low-rank and group sparsity structures. We implement this method using the alternating direction method of multipliers algorithm and conduct numerical studies to demonstrate its effectiveness across various datasets, including the ozone concentration and nitrogen oxide data.

키워드