Reduced Rank Multivariate Kernel Ridge Regression

Wenjia Wang; Yi-Hui Zhou

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arXiv · 2005.01559

Reduced Rank Multivariate Kernel Ridge Regression

Wenjia Wang·Yi-Hui Zhou

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Abstract

In the multivariate regression, also referred to as multi-task learning in machine learning, the goal is to recover a vector-valued function based on noisy observations. The vector-valued function is often assumed to be of low rank. Although the multivariate linear regression is extensively studied in the literature, a theoretical study on the multivariate nonlinear regression is lacking. In this paper, we study reduced rank multivariate kernel ridge regression, proposed by \cite{mukherjee2011reduced}. We prove the consistency of the function predictor and provide the convergence rate. An algorithm based on nuclear norm relaxation is proposed. A few numerical examples are presented to show the smaller mean squared prediction error comparing with the elementwise univariate kernel ridge regression.

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Wenjia Wang, Yi-Hui Zhou. 2020-05-04. Reduced Rank Multivariate Kernel Ridge Regression. https://arxiv.org/abs/2005.01559

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