高斯回归权重空间过程

高斯回归权重空间过程

笔记来源：https://www.bilibili.com/video/av70839977/?p=115

参考文献：

学习文献1
https://ww2.mathworks.cn/help/stats/gaussian-process-regression-models.html
http://smellysheep.com/2018/07/%E9%AB%98%E6%96%AF%E8%BF%87%E7%A8%8B%E5%9B%9E%E5%BD%92/

$(A+U C V)^{-1}=A^{-1}-A^{-1} U\left(C^{-1}+VA^{-1} U\right)^{-1} V A^{-1}$(A+UCV)−1=A−1−A−1U(C−1+VA−1U)−1VA−1

方差：
$\Phi\left(x^{*}\right) \Sigma_{p} \Phi\left(x^{*}\right)-\Phi\left(x^{*}\right)^{T} \Sigma p \Phi^{\top}\left(k+\sigma^{2} I\right)^{-1} \Phi \Sigma p \Phi\left(x^{*}\right)$Φ(x∗)Σp​Φ(x∗)−Φ(x∗)TΣpΦ⊤(k+σ2I)−1ΦΣpΦ(x∗)
$k=\Phi\Sigma_{p}\Phi^{T}\\ \Phi(x^*)^T\Sigma_p\Phi^T\\ \Phi(x^*)\Sigma_p\Phi(x^*)\\ \Phi\Sigma_p\Phi(x^*)$k=ΦΣp​ΦTΦ(x∗)TΣp​ΦTΦ(x∗)Σp​Φ(x∗)ΦΣp​Φ(x∗)