StatNMoE-class {meteorits}

A Reference Class which contains statistics of a NMoE model.

Description

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.

Fields

piik

Matrix of size (n, K) representing the probabilities \pi_{k}(x_{i}; \boldsymbol{\Psi}) = P(z_{i} = k | \boldsymbol{x}; \Psi) of the latent variable z_{i}, i = 1,\dots,n.

z_ik

Hard segmentation logical matrix of dimension (n, K) obtained by the Maximum a posteriori (MAP) rule: z\_ik = 1 \ \textrm{if} \ z\_ik = \textrm{arg} \ \textrm{max}_{s} \ \tau_{is};\ 0 \ \textrm{otherwise}, k = 1,\dots,K.

klas

Column matrix of the labels issued from z_ik. Its elements are klas(i) = k, k = 1,\dots,K.

tik

Matrix of size (n, K) giving the posterior probability \tau_{ik} that the observation y_{i} 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 | \boldsymbol{x}, \boldsymbol{\Psi}), i = 1,\dots,n.

log_sum_piik_fik

Column matrix of size m giving the values of \textrm{log} \sum_{k = 1}^{K} P(y_{i}, \ z_{i} = k | \boldsymbol{x}, \boldsymbol{\Psi}), i = 1,\dots,n.

Methods

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 \ \textrm{if} \ k = \textrm{arg} \ \textrm{max}_{s} \ \tau_{is};\ 0 \ \textrm{otherwise}

See Also

ParamNMoE