[Math] Example calculation of estimating GMM parameters using EM

expectationnormal distributionoptimizationstatistics

I'm trying to study expectation maximization and I've almost got the idea. What I'm missing is a concrete example. Could someone familiar with the subject give me a concrete example how one would apply expectation maximization algorithm for Gaussian mixture models?

I have tried to google for examples, but it seems to be difficult to find a good one. Could you show all the theoretical steps and then apply the steps with a numerical example? You don't need to repeat the algorithm for many iterations, one is enough 🙂

If this question is too long to answer might someone give me references where I could find a good and clear examples?

Thnx for any help!

Best Answer

This is a quick reference to mixture models and EM: it is helpful to fix notation and it describes the link between EM and k-means. Here, at paragraph 4 you can find an example involving Gaussian mixtures with some computations involving sampling and subsequent outcome analysis.

If you are interested also in generalized linear mixture models, please have a look at chapter 3 of this book: there is a description of likelihood inference via EM, numerical simulations and sampling.

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