Introduction to the EM algorithm - Department of Statistics

And finally in the same way using Lagrange multipliers and the restriction
that ∑ M
j=1 α j = 1 we have:
ˆα j = 1 n
n∑
i=1
p (k)
ij
.
The updates are as follows:
= ˆµ j
σ 2 (k+1)
j
is ˆσ
j 2 with µ j = µ (k+1)
j
;
α (k+1)
j
= ˆα j .
µ (k+1)
j
We iterate the E-step and M-step till convergence.
Camila Souza (UBC) Introduction to the EM algorithm November 2010 22 / 25