Gaussian Mixture Model: the initial means and variances of two clusters in a GMM are as follows:...

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Statistics

Gaussian Mixture Model:
the initial means and variances of two clusters in a GMM are asfollows: ?(1)=âˆ’3, ?(2)=2, ?21=?22=4. Let ?1=?2=0.5.
Let ?(1)=0.2, ?(2)=âˆ’0.9, ?(3)=âˆ’1, ?(4)=1.2, ?(5)=1.8 be fivepoints that need to cluster.
Need to find
1) p(1|1)
2) p(1|2)
3) p(1|3)
4) p(1|4)
5) p(1|5)

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4.5 Ratings (690 Votes)

Initial derivationsWe are now going to introduce some additional notation Just aword of warning Math is coming on Dont worry Ill try to keepthe notation as clean as possible for better understanding of thederivations First lets suppose we want to know what is theprobability that a data point xn comesfrom Gaussian k We can express this asWhich reads given a datapoint x what is the probability it camefrom Gaussian k In this case z is alatent variable that takes only two possible values It isone when x came from Gaussian k and zerootherwise Actually we dont get to see this z variablein reality but knowing its probability of occurrence will beuseful in helping us determine the Gaussian mixture parameters aswe See Answer

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