Derivation of GMM
Derivation of one single-variable gaussian distribution
Considering a generative model, let $P$ denote the generated probability distribution, ${x}_{i=1}^n$ denote the data set, and $\mu$ and $\sigma$ denotes the parameters of a generated Gaussian Distribution. We will go over a max-likelihood process to find the parameters of the generated distribution.
Independence Assumption: $x_i\perp x_j\ \forall i,j \ \mbox{s.j} \ 1\le i,j\le n$
Result of one multi-variable gaussian distribution
Multi-variate Gaussian Distribution Probability Function
Result of EM algorithm
Gaussian Mixture
Latent Variable
Result
Ref
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