ABSTRACT
To re-estimate ck,„, and tm we note that they are related only to Qz. Furthermore, only includes 4)„, and tm . The relevant partial derivatives are
En pn (k)(ez (k))Tr] 1 En [xn (k)]Tr 1 . En[xn (k)] En[xn (k)(xri (k))Tr]
and
N aQa
(-4,---24.7n Egg-, — Crnr,tm — tme; + Kntmt,70 • col (10.66) n=1
N (10.67) = — 4)m) E — 4.7ne;';1 - — 4.7n)trn} • gin•
n=1
Setting the above derivatives to zero, we obtain the re-estimate for and tm:
N = {E (CI - bmtm — Knirnifr,n) • gild
n=1 N
• IE(13','„ — cmtm — + Knimimr` ) • cp'70-1 (10.68) n=1
and - )-1 — • (-4 tn, = (10.69)
Kn • COin In the above re-estimation, the parameters .1.„, and tm are updated alternatively at
separate EM iterations. This gives rise to the generalized EM algorithm, which gives local optimization in the M-step, rather than global optimization.
