Introduction to the EM algorithm - Department of Statistics
Introduction to the EM algorithm - Department of Statistics
Introduction to the EM algorithm - Department of Statistics
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Applying <strong>the</strong> <strong>EM</strong> <strong>algorithm</strong><br />
E-step: Calculate Q(θ, θ (k) ) = E(log p(y, z|θ)|y, θ (k) ).<br />
Note: Maybe a better notation for this expectation would be<br />
E θ (k)(log p(y, z|θ)|y).<br />
The complete data log-likelihood can be written as:<br />
log p(y, z|θ) = log p(y|z, θ) + log p(z|α’s)<br />
=<br />
n∑<br />
n∑<br />
log p(y i |z i , λ zi ) + log α zi<br />
i=1<br />
i=1<br />
= L 1 (λ’s) + L 2 (α’s). (4)<br />
Camila Souza (UBC) <strong>Introduction</strong> <strong>to</strong> <strong>the</strong> <strong>EM</strong> <strong>algorithm</strong> November 2010 16 / 25