标题： 高斯过程的精度和乔列斯基因子估计 显示英文标题

标题： Precision and Cholesky Factor Estimation for Gaussian Processes

摘要： 本文研究了通过在多个位置观测高斯过程所得到的大精度矩阵和Cholesky分解因子的估计问题。在关于精度矩阵和观测值的一般假设下，我们证明了样本复杂度以对数多项式的方式依赖于精度矩阵及其Cholesky因子的大小。这些估计任务的关键挑战在于目标矩阵的条件数随其尺寸呈多项式增长。对于精度矩阵的估计，我们的理论基于一种直观的格图局部回归技术，该技术利用了由筛选效应暗示的近似稀疏性。对于Cholesky因子的估计，我们利用了一种最近用于建立稀疏Cholesky分解复杂度界的方法——块状Cholesky分解。 显示英文摘要

摘要： This paper studies the estimation of large precision matrices and Cholesky factors obtained by observing a Gaussian process at many locations. Under general assumptions on the precision and the observations, we show that the sample complexity scales poly-logarithmically with the size of the precision matrix and its Cholesky factor. The key challenge in these estimation tasks is the polynomial growth of the condition number of the target matrices with their size. For precision estimation, our theory hinges on an intuitive local regression technique on the lattice graph which exploits the approximate sparsity implied by the screening effect. For Cholesky factor estimation, we leverage a block-Cholesky decomposition recently used to establish complexity bounds for sparse Cholesky factorization.