Assume we choose the same prior distribution for a GMM as in Example 14.3.1. Use the EM

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Assume we choose the same prior distribution for a GMM as in Example 14.3.1. Use the EM algorithm to derive the MAP estimation for GMMs:

a. Give the formulae to update all GMM parameters MAP iteratively.

b. If we approximate the true posterior distribution of a GMM p¹jxº by another approximate distribution q˜¹º as q˜¹º / p¹ºQ¹jMAPº, where Q¹º is the auxiliary function in the EM algorithm, derive this approximate posterior distribution q˜¹º, and compare it with the variational distribution q¹º in Example 14.3.1.

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