论文标题
降低等级多元内核脊回归
Reduced Rank Multivariate Kernel Ridge Regression
论文作者
论文摘要
在机器学习中也称为多任务学习的多元回归中，目标是基于嘈杂的观测值恢复矢量值函数。矢量值函数通常被假定为低等级。尽管在文献中对多元线性回归进行了广泛的研究，但缺乏关于多元非线性回归的理论研究。在本文中，我们研究了\ cite {mukherjee2011 reded}提出的等级多变量内核脊回归。我们证明了函数预测指标的一致性并提供了收敛速率。提出了基于核规范松弛的算法。提出了一些数值示例，以显示与元素式单变量内核脊回归相比的较小平方的预测误差。
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.
