格林函数的协方差矩阵及其在机器学习中的应用(CS LG)---Elva

本文提出并实现了一种基于格林函数理论的回归算法。本文首先研究了二阶线性常微分方程Dirichlet边值问题的Green函数，它是适合Hilbert空间的再生核。接下来我们考虑一个由归一化格林函数组成的协方差矩阵，它被看作是概率密度函数。通过贝叶斯方法，协方差矩阵给出了具有预测均值的预测分布μ以及置信区间[μ-2s, μ+2s]，其中s代表标准差。

原文题目：The covariance matrix of Green's functions and its application to machine learning

原文：In this paper, a regression algorithm based on Green's function theory is proposed and implemented. We first survey Green's function for the Dirichlet boundary value problem of 2nd order linear ordinary differential equation, which is a reproducing kernel of a suitable Hilbert space. We next consider a covariance matrix composed of the normalized Green's function, which is regarded as aprobability density function. By supporting Bayesian approach, the covariance matrix gives predictive distribution, which has the predictive mean μ and the confidence interval [μ-2s, μ+2s], where s stands for a standard deviation.

原文作者：Tomoko Nagai

原文地址：https://arxiv.org/abs/2004.06481