一維的高斯分佈(或常態分佈) $X \sim N(\mu,\sigma^2 )$
PDF: p(x)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSMUxvXyn8fAzHvBqzpLiQt-sW_yzClffA3Y4gEx-CvOtZ7_9hnN-ysGuyzzrtOpgLeWV1YwxrEH1nbBNNvdcgu9q5phJ-r9As2Ccjxwjrqh-FY4VN0U3K6u8gbEELqwXpUKpvTgElKdI/s640/gaussian.png)
二維的高斯分佈 $ N\sim(\mu,\sum ) $
PDF: p(x,y)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHvXRdGi0f4ykFrsA7cXrtQYsJHdEth7pnEQO1pPD83WenBgqgqkL74Y65Do4Ttq7bVW2Kroe2T-IpIdxU5Bkv3RCt23FXkpwAMiVIcBijR9vfl-EPo3cu85gSBj2ebUbie9sL45CGxhg/s640/Illustration-of-a-bivariate-Gaussian-distribution-The-marginal-and-joint-probability.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEir2f0X87WvvzFgbyRT-LQD38eTcipPSIQUCJBdWsOzujcyV6nG4Ul4Jxvm9xXoOukII1iSTEj0gR-7fZKUh6mtnZwVNEIKnbFBnJLOj3DafvpXtV8zamv1gWSr_GoXs6Wwse6rsgHFo5M/s640/bivariate1.png)
![MultivariateNormal.png](https://upload.wikimedia.org/wikipedia/commons/thumb/8/8e/MultivariateNormal.png/300px-MultivariateNormal.png)
Many sample points from a multivariate normal distribution with and , shown along with the 3-sigma ellipse, the two marginal distributions, and the two 1-d histograms.
μ ∈ Rk — location
Σ ∈ Rk × k — covariance
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgznc_sBzKDWMaXvJlHz5HQs6I6B3pzNPG1NZoREuRiG5Ane3cImXHDygcFqJKriszX2kkJfJf3mocgk3v05dYcliMC0C92zncdT6XNVgklC0uracChI0Qwv-bFOvEnG7uS-6nraRfPJZ8/s1600/convarince_formula.png)
References:
- WiKi-Multivariate normal distribution
https://en.wikipedia.org/wiki/Multivariate_normal_distribution - 吳恩達-機器學習(9)-異常檢測、協同過濾https://www.itread01.com/content/1545204306.html
- Andrew Ng
https://www.coursera.org/learn/machine-learning?action=enroll#syllabus - Python for Covvriance
https://hadrienj.github.io/posts/Preprocessing-for-deep-learning/
沒有留言 :
張貼留言