EM of GMM appendix (M-Step full derivations)
5 min readSep 21, 2020
This article is an extension of “Gaussian Mixture Models and Expectation-Maximization (A full explanation)”. If you didn’t read it, this article might not be very useful.
The goal here is to derive the closed-form expressions necessary for the update of the parameters during the Maximization step of the EM algorithm applied to GMMs. This material was written as a separate article in order not to overload the main one.
Ok so recall that during the M-Step, we want to maximize the following lower bound with respect to Θ :
