论文标题
格林功能的协方差矩阵及其在机器学习中的应用
The covariance matrix of Green's functions and its application to machine learning
论文作者
论文摘要
在本文中，提出并实施了基于格林功能理论的回归算法。我们首先调查了绿色的功能，用于第二阶线性普通微分方程的Dirichlet边界值问题，这是合适的Hilbert空间的再现核。接下来，我们考虑由归一化绿色函数组成的协方差矩阵，该函数被视为差异密度函数。通过支持贝叶斯方法，协方差矩阵给出了预测性分布，该分布具有预测性平均值$μ$和置信区间[$μ$ -2S，$μ$+2s]，其中S代表标准偏差。
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.
