StatMRHLP-class {samurais}

A Reference Class which contains statistics of a MRHLP model.

Description

StatMRHLP contains all the statistics associated to a MRHLP 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 at each step of the algorithm and the obtained values of model selection criteria..

Fields

pi_ik

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

z_ik

Hard segmentation logical matrix of dimension (m, K) obtained by the Maximum a posteriori (MAP) rule: z\_ik = 1 \ \textrm{if} \ z\_ik = \textrm{arg} \ \textrm{max}_{s} \ \pi_{s}(x_{i}; \boldsymbol{\Psi});\ 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.

tau_ik

Matrix of size (m, K) giving the posterior probability that the observation Y_{i} originates from the k-th regression model.

polynomials

Array of size (m, d, K) giving the values of the estimated polynomial regression components.

weighted_polynomials

Array of size (m, d, K) giving the values of the estimated polynomial regression components weighted by the prior probabilities pi_ik.

Ex

Matrix of size (m, d). Ex is the curve expectation (estimated signal): sum of the polynomial components weighted by the logistic probabilities pi_ik.

loglik

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

com_loglik

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

stored_loglik

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

stored_com_loglik

Numeric vector. Stored values of the Complete 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 (m, K) giving the values of the logarithm of the joint probability P(y_{i}, \ z_{i} = k | \boldsymbol{x}, \boldsymbol{\Psi}), i = 1,\dots,m.

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,m.

Methods

computeLikelihood(reg_irls)

Method to compute the log-likelihood. reg_irls is the value of the regularization part in the IRLS algorithm.

computeStats(paramMRHLP)

Method used in the EM algorithm to compute statistics based on parameters provided by the object paramMRHLP of class ParamMRHLP.

EStep(paramMRHLP)

Method used in the EM algorithm to update statistics based on parameters provided by the object paramMRHLP of class ParamMRHLP (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} \ \pi_{s}(x_{i}; \boldsymbol{\Psi});\ 0 \ \textrm{otherwise}

See Also

ParamMRHLP