ParamMixRHLP-class: A Reference Class which contains parameters of a mixture of RHLP models.

Description

ParamMixRHLP contains all the parameters of a mixture of RHLP models.

Arguments

Fields

fData: FData object representing the sample (covariates/inputs X and observed responses/outputs Y).

K

The number of clusters (Number of RHLP models).

R

The number of regimes (RHLP components) for each cluster.

p

The order of the polynomial regression.

q

The dimension of the logistic regression. For the purpose of segmentation, it must be set to 1.

variance_type

Character indicating if the model is homoskedastic (variance_type = "homoskedastic") or heteroskedastic (variance_type = "heteroskedastic"). By default the model is heteroskedastic.

alpha

Cluster weights. Matrix of dimension \((1, K)\).

W

Parameters of the logistic process. \(\boldsymbol{W} = (\boldsymbol{w}_{1},\dots,\boldsymbol{w}_{K})\) is an array of dimension \((q + 1, R - 1, K)\), with \(\boldsymbol{w}_{k} = (\boldsymbol{w}_{k,1},\dots,\boldsymbol{w}_{k,R-1})\), \(k = 1,\dots,K\), and q the order of the logistic regression. q is fixed to 1 by default.

beta

Parameters of the polynomial regressions. \(\boldsymbol{\beta} = (\boldsymbol{\beta}_{1},\dots,\boldsymbol{\beta}_{K})\) is an array of dimension \((p + 1, R, K)\), with \(\boldsymbol{\beta}_{k} = (\boldsymbol{\beta}_{k,1},\dots,\boldsymbol{\beta}_{k,R})\), \(k = 1,\dots,K\), p the order of the polynomial regression. p is fixed to 3 by default.

sigma2

The variances for the K clusters. If MixRHLP model is heteroskedastic (variance_type = "heteroskedastic") then sigma2 is a matrix of size \((R, K)\) (otherwise MixRHLP model is homoskedastic (variance_type = "homoskedastic") and sigma2 is a matrix of size \((K, 1)\)).

nu

The degree of freedom of the MixRHLP model representing the complexity of the model.

phi

A list giving the regression design matrices for the polynomial and the logistic regressions.

Methods

CMStep(statMixRHLP, verbose_IRLS = FALSE): Method which implements the M-step of the CEM algorithm to learn the parameters of the MixRHLP model based on statistics provided by the object statMixRHLP of class StatMixRHLP (which contains the E-step and the C-step).

initParam(init_kmeans = TRUE, try_algo = 1)

Method to initialize parameters alpha, W, beta and sigma2.

If init_kmeans = TRUE then the curve partition is initialized by the R-means algorithm. Otherwise the curve partition is initialized randomly.

If try_algo = 1 then beta and sigma2 are initialized by segmenting the time series Y uniformly into R contiguous segments. Otherwise, W, beta and sigma2 are initialized by segmenting randomly the time series Y into R segments.

initRegressionParam(Yk, k, try_algo = 1)

Initialize the matrix of polynomial regression coefficients beta_k for the cluster k.

MStep(statMixRHLP, verbose_IRLS = FALSE)

Method which implements the M-step of the EM algorithm to learn the parameters of the MixRHLP model based on statistics provided by the object statMixRHLP of class StatMixRHLP (which contains the E-step).