Bayesian Priors
x 2 ) = 1 ni T t =1 Pr(i | xt )x 2 t .(10)
This is the same as the expectation step in the EM algorithm. Finally, these new sufficient statistics from the training **data** are used to update the old UBM sufficient statistics for mixture i to create the adapted parameters for mixture i (Fig. 3b) with the equations:
wi = α w i ni /T + (1 − α w i )wi γ (11) µi = α m i Ei(x) + (1 − α m i )µi (12) σ 2 i = α v i Ei(x 2 ) + (1 − α v i )(σ 2 i + µ 2 i ) −μ 2 i .(13)
The adaptation coefficients controlling the balance between old and new estimates are {α w i , α m i , α v i } for the weights, means and variances, respectively. The scale factor, γ , is computed over all adapted mixture weights to ensure they sum to unity. Note that the sufficient statistics, not the derived parameters, such as the variance, are being adapted.