cbfinn / gps

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How do you compute the variance in the m-step of GMM ?? #126

Closed Shunichi09 closed 2 years ago

Shunichi09 commented 2 years ago

Hi, Thank you for sharing your great code. I have a question about how you compute the variance in the m-step of GMM.

I think the em-algorithm of GMM is as follows, (referring to the PRML)

image

image

also in sk-learn,

https://github.com/scikit-learn/scikit-learn/blob/da1079046c4de9574ec15fd83335dc0f9b9cab69/sklearn/mixture/_gaussian_mixture.py#L154

In your code, although the mean and responsibility computation is the same as above, about the variance

https://github.com/cbfinn/gps/blob/82fa6cc930c4392d55d2525f6b792089f1d2ccfe/python/gps/utility/gmm.py#L201

I tried to understand your computation, but I could not... Is it possible to share how you got the code to estimate the variance ??

Again, thanks.