Efficient training of Gaussian processes with tensor product structure
针对协方差矩阵为多个Kronecker乘积之和的高斯过程，提出基于张量列格式和Krylov子空间方法的高效超参数优化方案，解决大数据量下的线性系统和迹估计问题。
Abstract To determine the optimal set of hyperparameters of a Gaussian process based on a large number of training data, both a linear system and a trace estimation problem must be solved. In this paper, we focus on establishing numerical methods for the case where the covariance matrix is given as the sum of possibly multiple Kronecker products, i.e., can be identified as a tensor. As such, we will represent this operator and the training data in the tensor train format. Based on the AME n method and Krylov subspace methods, we derive an efficient scheme for computing the matrix functions required for evaluating the gradient and the objective function in hyperparameter optimization.