2020/05/04 by Wenjia Wang, Wang, Wenjia, Yi‐Hui Zhou +2
Computer Science · Engineering · Mathematics · #Artificial intelligence #Bayesian multivariate linear regression #Combinatorics #Computer science #Consistency (knowledge bases) #FOS: Computer and information sciences #FOS: Mathematics #Face and Expression Recognition #Kernel (algebra) #Kernel method #Mathematics #Methodology (stat.ME) #Multivariate statistics #Nonparametric regression #Regression #Regression analysis #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistics #Statistics Theory (math.ST) #Support vector machine #Univariate #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.2005.01559
arxiv created 2020/05/04 · openalex publication_date 2020/05/04 · arxiv updated 2020/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citemukherjee2011reduced. 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.