Reduced Rank Multivariate Kernel Ridge Regression
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.
Cite
@article{arxiv.2005.01559,
title = {Reduced Rank Multivariate Kernel Ridge Regression},
author = {Wenjia Wang and Yi-Hui Zhou},
journal= {arXiv preprint arXiv:2005.01559},
year = {2020}
}