2021-11-18

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协方差, 协方差矩阵 *

(*:相关内容在此之前已经出现过)


这里补充了一些协方差计算的例题

🔗 [2022-08-07 - Truxton's blog] https://truxton2blog.com/2022-08-07/#协方差、协方差矩阵的计算(附带例题)

简单理解:

协方差是一个反映两个随机变量相关程度的指标,如果一个变量跟随着另一个变量同时变大或者变小,那么这两个变量的协方差就是正值,反之相反。

https://www.zhihu.com/question/19734616/answer/117730676

协方差入门讲解视频:🔗 [Covariance, Clearly Explained!!! - YouTube] https://www.youtube.com/watch?v=qtaqvPAeEJY

covariance>0的情况
covariance<0的情况
covariance=0的情况(注意第3张图)

Covariance>0,Covariance<0,Covariance=0的情况如上面3张图所示。要注意Covariance数值的大小不能用来表示斜率、远近等性质,只能用来做后续的计算。

这个视频也讲类似的内容,但附加了weight,同时更公式化一些:🔗 [The covariance matrix - YouTube] https://www.youtube.com/watch?v=WBlnwvjfMtQ


协方差矩阵

https://www.zhihu.com/question/24283387

MIR相关

🔗 [计算音乐基础知识 - 知乎] https://zhuanlan.zhihu.com/p/61287265

🔗 [MIR(二) - Beat Tracking - 知乎] https://zhuanlan.zhihu.com/p/366724962

novelty score以及其他内容 🔗 [论文阅读13 - 知乎] https://zhuanlan.zhihu.com/p/41068720

高斯过程


2022-08-04更新:

我觉得之前列举的这些资源还不够直观入门,现在更新一个更加入门的:

A Gaussian Process(GP) is a probability distribution over functions.

https://roboticsknowledgebase.com/wiki/math/gaussian-process-gaussian-mixture-model/
https://stats.stackexchange.com/questions/376141/what-is-a-distribution-over-functions
https://www.researchgate.net/figure/Illustration-of-1-D-Gaussian-process-A-Gaussian-process-is-a-statistical-model-that_fig44_325386879

从最原始的二维正态分布开始,用图像一步一步解释高斯过程:🔗 [图文详解高斯过程(一)——含代码 - 知乎] https://zhuanlan.zhihu.com/p/32152162
注意:这篇文章是翻译的,英文原文见:🔗 [AB - Introduction to Gaussian Processes - Part I] http://bridg.land/posts/gaussian-processes-1
注意:原作者提到过有更优化的解决方案part II,但是鸽了

https://zhuanlan.zhihu.com/p/32152162

比如:

http://bridg.land/posts/gaussian-processes-1

高斯过程的直观表示(数据图像、曲线形状):🔗 [Gaussian Process - Regression - Part 1 - Kernel First - YouTube] https://www.youtube.com/watch?v=lWNy71IC8CU

🔗 [高斯过程 Gaussian Processes 原理、可视化及代码实现 - 知乎] https://zhuanlan.zhihu.com/p/75589452

🔗 [svm - Can someone explain the RBF Kernel to me? - Cross Validated] https://stats.stackexchange.com/questions/300434/can-someone-explain-the-rbf-kernel-to-me

🔗 [machine learning - What will be the input value (i.e. $x$ and $x′$) of RBF kernel for a given dataset or data matrix $x$? - Cross Validated] https://stats.stackexchange.com/questions/220718/what-will-be-the-input-value-i-e-x-and-x-of-rbf-kernel-for-a-given-datas



 Last Modified in 2022-08-14 

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