Multivariate Gaussian

Creator
Creator
Seonglae ChoSeonglae Cho
Created
Created
2024 Oct 14 9:29
Editor
Edited
Edited
2024 Nov 18 11:59
Refs

Multivariate Normal Distribution, Joint Normal Distribution

It is a single distribution and GMM is multiple.
Each random variable normally distributed, at the same time joint multi-variable normally distributed
Covariance Matrix
affects exponential part of
Probability Density Function

Conditional Mean

가 주어졌을 때 의 평균이 어떻게 이동하는지
generalized form with minus except notation
generalized form with range notation
multi to multi with dimension analysis if we choose k variables for left side

Conditional Variance

generalized form with minus except notation
generalized form with range notation
multi to multi with dimension analysis if we choose k variables for left side

Inverse matrix

If the covariance matrix is singular, it means that the random variables are fully constrained or deterministic, not truly random. For example, if , then the distribution of would collapse into a plane, not a proper 3D Gaussian distribution.
 
 
 
 
 
 

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