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Expectation Maximization algorithm for gamma mixture model

Posted on 2011-03-18
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Last Modified: 2012-05-11
I'm looking for an Expectation Maximization(EM) algorithm for estimating paramers of gamma mixture model . The distribution is givin in the image The required form of gamma density
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Question by:00matrix00
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8 Comments
 
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Expert Comment

by:TommySzalapski
ID: 35172682
There's only one Expectation Maximization algorithm. It's explained fairly well here http://www.cc.gatech.edu/~dellaert/em-paper.pdf.
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Author Comment

by:00matrix00
ID: 35172900
Actually what I want is how I update the parameters required for the gamma distribution in the Maximization step of EM
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Expert Comment

by:TommySzalapski
ID: 35172934
how I update the parameters
You just start with an initial guess for the expectation step and the maximization step gives the new guess. So you just plug the new guess in.
If that's not what you mean, then can you give more detail including you expectation step?
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Author Comment

by:00matrix00
ID: 35172940
I mean that I want the exact formula for updating these two parameters
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LVL 37

Expert Comment

by:TommySzalapski
ID: 35173423
Can you post what you have so far (especially your Expectation step) so that I don't go a different direction and cause confusion?
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Author Comment

by:00matrix00
ID: 35175025
In the Expectation step, I should compute the member ship probability using the form (Attached ). How can I update the three paramters of gamma mixture model in the maximization step.

Thanks MemberShipProbability
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Author Comment

by:00matrix00
ID: 35177084
Thank U TommySzalapski,
Actually, I found the formula for updating the parameters. The problem now is how to generate an initial value for these paramters. I trying to use random intialization for them but when I implemented , the pdf generated using EM didn't the fitted data histogram.
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Accepted Solution

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TommySzalapski earned 500 total points
ID: 35177761
Random initialization is usually not good. Just pick an initial guess of .5 or something. You know your application, so just pick a guess that you think makes sense. Small positive numbers usually are safe bets to use as guesses. I would avoid guessing 0 for most things just in case.
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