Description Fields Methods See Also
StatNMoE contains all the statistics associated to a NMoE model. It mainly includes the E-Step of the EM 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 NMoE.
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 NMoE model.
com_loglik
Numeric. Complete-data log-likelihood of the NMoE model.
stored_loglik
Numeric vector. Stored values of the log-likelihood at each EM 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.
computeLikelihood(reg_irls)
Method to compute the log-likelihood. reg_irls
is the value of
the regularization part in the IRLS algorithm.
computeStats(paramNMoE)
Method used in the EM algorithm to compute statistics based on
parameters provided by the object paramNMoE
of class
ParamNMoE.
EStep(paramNMoE)
Method used in the EM algorithm to update statistics based on parameters
provided by the object paramNMoE
of class ParamNMoE
(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
ParamNMoE
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