1 - 東北大学

Maximization of Marginal Likelihood byEM AlgorithmrrrMarginalrr rrPr{ Y = y | α , σ } = ∑ Pr{ Y = y | X = z,σ }Pr{ X = x | α}Likelihoodrz(rQ α,σ α',σ',y)Q-Functionr r r rr r r r= ∑ Pr{ X = z | Y = y,α',σ'}lnPr{X = z,Y = y | α,σ}E - StepQM - Step:rzEM (Expectation Maximization) AlgorithmE-step and M-Step are iterated until convergence:( α , σ α () t , σ () t )← ∑ rz:rPr{ Xr r= z | Y =( α ( t + 1 ),σ ( t + 1))rry,α ( t),σ ( t)}ln Pr{ X←argmax( α , β )Q=r rz,Y=( α , σ α () t , σ () t ).ry | α , σ }10 June, 2009 CIVM200906 (Kyoto) 20