Introduction to the EM algorithm - Department of Statistics
Introduction to the EM algorithm - Department of Statistics
Introduction to the EM algorithm - Department of Statistics
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Derivation <strong>of</strong> <strong>the</strong> <strong>EM</strong> <strong>algorithm</strong><br />
The joint distribution <strong>of</strong> y and z (also called <strong>the</strong> complete data<br />
distribution) can be written as<br />
Rearranging this we get:<br />
Taking <strong>the</strong> logarithm we have<br />
p(y, z|θ) = p(z|y, θ)p(y|θ).<br />
p(y|θ) =<br />
p(y, z|θ)<br />
p(z|y, θ) .<br />
log p(y|θ) = log p(y, z|θ) − log p(z|y, θ).<br />
Camila Souza (UBC) <strong>Introduction</strong> <strong>to</strong> <strong>the</strong> <strong>EM</strong> <strong>algorithm</strong> November 2010 8 / 25
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