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Updating each
Gaussian definitely improves the
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probability of
generating the data if we generate
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it from the same
Gaussians after the parameter
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updates.
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But
we know that the posterior will change
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after
updating the parameters.
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A good way to
show that this is OK is to show
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that there is a
single function that is improved by
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both the E-step
and the M-step.
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The
function we need is called Free Energy.
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