Description Fields Methods See Also

StatTMoE contains all the statistics associated to a TMoE model. It mainly includes the E-Step of the ECM algorithm calculating the posterior distribution of the hidden variables, as well as the calculation of the log-likelhood.

`piik`

Matrix of size

*(n, K)*representing the probabilities*π_{k}(x_{i}; Ψ) = P(z_{i} = k | x; Ψ)*of the latent variable*z_{i}, i = 1,…,n*.`z_ik`

Hard segmentation logical matrix of dimension

*(n, K)*obtained by the Maximum a posteriori (MAP) rule:*z_ik = 1 if z_ik = arg max_s τ_{is}; 0 otherwise*,*k = 1,…,K*.`klas`

Column matrix of the labels issued from

`z_ik`

. Its elements are*klas(i) = k*,*k = 1,…,K*.`tik`

Matrix of size

*(n, K)*giving the posterior probability*τik*that the observation*yi*originates from the*k*-th expert.`Ey_k`

Matrix of dimension

*(n, K)*giving the estimated means of the experts.`Ey`

Column matrix of dimension

*n*giving the estimated mean of the TMoE.`Var_yk`

Column matrix of dimension

*K*giving the estimated means of the experts.`Vary`

Column matrix of dimension

*n*giving the estimated variance of the response.`loglik`

Numeric. Observed-data log-likelihood of the TMoE model.

`com_loglik`

Numeric. Complete-data log-likelihood of the TMoE model.

`stored_loglik`

Numeric vector. Stored values of the log-likelihood at each ECM iteration.

`BIC`

Numeric. Value of BIC (Bayesian Information Criterion).

`ICL`

Numeric. Value of ICL (Integrated Completed Likelihood).

`AIC`

Numeric. Value of AIC (Akaike Information Criterion).

`log_piik_fik`

Matrix of size

*(n, K)*giving the values of the logarithm of the joint probability*P(y_{i}, z_{i} = k | x, Ψ)*,*i = 1,…,n*.`log_sum_piik_fik`

Column matrix of size

*m*giving the values of*log ∑_{k = 1}^{K} P(y_{i}, z_{i} = k | x, Ψ)*,*i = 1,…,n*.`Wik`

Conditional expectations

*wik*.

`computeLikelihood(reg_irls)`

Method to compute the log-likelihood.

`reg_irls`

is the value of the regularization part in the IRLS algorithm.`computeStats(paramTMoE)`

Method used in the ECM algorithm to compute statistics based on parameters provided by the object

`paramTMoE`

of class ParamTMoE.`EStep(paramTMoE)`

Method used in the ECM algorithm to update statistics based on parameters provided by the object

`paramTMoE`

of class ParamTMoE (prior and posterior probabilities).`MAP()`

MAP calculates values of the fields

`z_ik`

and`klas`

by applying the Maximum A Posteriori Bayes allocation rule.*z_{ik} = 1 if z_ik = arg max_{s} τ_{is}; 0 otherwise*

ParamTMoE

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