Chunk #65 — Online Methods — Estimate π by maximum likelihood.
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To simplify notation, let Σk,l:=ωlUk, and replace the double index k,l with a single index p ranging from 1 to P≔KL, so that eqs. 3 & 4 become p(bj | π, U)=∑p=1PπpNR(bj;0,Σp), p(b^j | π, U,Vj)=∑p=1PπpNR(b^j;0, Σp+Vj).