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https://frankccccc.github.io/blog/
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From EM To VBEM | Golden Hat #3

Open utterances-bot opened 10 months ago

utterances-bot commented 10 months ago

From EM To VBEM | Golden Hat

  1. Introduction When we use K-Means or GMM to solve clustering problem, the most important hyperparameter is the number of the cluster. It is quite hard to decide and cause the good/bad performance significantly. In the mean time, K-Means also cannot handle unbalanced dataset well. However, the variational Bayesian Gaussian mixture model(VB-GMM) can solve these. VB-GMM is a Bayesian model that contains priors over the parameters of GMM. Thus, VB-GMM can be optimized by variational Bayesian expectation maximization(VBEM) and find the optimal cluster number automatically.

https://frankccccc.github.io/blog/posts/from_em_to_vbem/

alephpi commented 10 months ago

According to The Variational Bayesian EM Algorithm for Incomplete Data: With Application to Scoring Graphical Model Structures, formula (7), you missed a factor $$p(\theta|\lambda)$$ in M Step update formula of the variational distribution on $$\theta$$