Parameters that best describe P can be obtained by maximizing the log likelihood with respect to the Gaussian mixture models (GMM) for all the frames of the speech [2].
We seek the optimal solution of hyperparameters by maximizing the log marginal likelihood (see [27] for details): log p ( Ψ ′ | s, θ ) = − 1 2 Ψ ′ T K Ψ ′ − 1 Ψ ′ − 1 2 log | K Ψ ′ | − n 2 log 2 Π, (11).
Now, by maximizing the log marginal likelihood and then differentiating with respect to Ξ j and ξ 0 and setting to zero yields (boldsymbol{Xi}_{j})^{new}=frac{J-boldsymbol{Xi}_{j} sum_{j=1}^{J} boldsymbol{Sigma}^{n}_{c^,c^,i,j}}{sum_{j=1}^{J}left(boldsymbol{mu}^{n}_{c^,c^,i,j}right)^{2}}, (29).
Given a sampling of the configurations after the clustering phase, we learn parameters by maximizing the log likelihood where θ={λ1, λ2, λ3} is the set of parameters.
The power transformation parameter, λ0, was obtained through a grid search by maximizing the log likelihood of the residual for the transformed response variable after removing the overall means.
The binary clinical variable, y, can be predicted using the logistic model: (1) Prob (y = 1 | X ; β ) = 1 1 + e - X β The parameter β can be estimated by maximizing the log likelihood function of the logistic model.
