multivariate Gaussian distribution

一維的高斯分佈(或常態分佈) $X \sim N(\mu,\sigma^2 )$

PDF:  p(x)


二維的高斯分佈 $ N\sim(\mu,\sum ) $
PDF:  p(x,y)



 



Many sample points from a multivariate normal distribution with ${\displaystyle {\boldsymbol {\mu }}=\left[{\begin{smallmatrix}0\\0\end{smallmatrix}}\right]}$ and ${\displaystyle {\boldsymbol {\Sigma }}=\left[{\begin{smallmatrix}1&3/5\\3/5&2\end{smallmatrix}}\right]}$, shown along with the 3-sigma ellipse, the two marginal distributions, and the two 1-d histograms.

μ ∈ R^k — location
Σ ∈ R^k × k — covariance 

References:

1. WiKi-Multivariate normal distribution
   https://en.wikipedia.org/wiki/Multivariate_normal_distribution
2. 吳恩達-機器學習(9)-異常檢測、協同過濾https://www.itread01.com/content/1545204306.html
3. Andrew Ng
   https://www.coursera.org/learn/machine-learning?action=enroll#syllabus
4. Python for Covvriance
   https://hadrienj.github.io/posts/Preprocessing-for-deep-learning/