ParamSNMoE-class: A Reference Class which contains parameters of a SNMoE model.

Description

ParamSNMoE contains all the parameters of a SNMoE model.

Arguments

Fields

X: Numeric vector of length n representing the covariates/inputs \(x_{1},\dots,x_{n}\).

Y

Numeric vector of length n representing the observed response/output \(y_{1},\dots,y_{n}\).

n

Numeric. Length of the response/output vector Y.

K

The number of experts.

p

The order of the polynomial regression for the experts.

q

The order of the logistic regression for the gating network.

alpha

Parameters of the gating network. \(\boldsymbol{\alpha} = (\boldsymbol{\alpha}_{1},\dots,\boldsymbol{\alpha}_{K-1})\) is a matrix of dimension \((q + 1, K - 1)\), with q the order of the logistic regression for the gating network. q is fixed to 1 by default.

beta

Polynomial regressions coefficients for each expert. \(\boldsymbol{\beta} = (\boldsymbol{\beta}_{1},\dots,\boldsymbol{\beta}_{K})\) is a matrix of dimension \((p + 1, K)\), with p the order of the polynomial regression. p is fixed to 3 by default.

sigma2

The variances for the K mixture components (matrix of size \((1, K)\)).

lambda

The skewness parameters for each experts (matrix of size \((1, K)\)).

delta

delta is equal to \(\delta = \frac{\lambda}{\sqrt{1+\lambda^2}}\).

df

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

Methods

initParam(segmental = FALSE)

Method to initialize parameters alpha, beta and sigma2.

If segmental = TRUE then alpha, beta and sigma2 are initialized by clustering the response Y uniformly into K contiguous segments. Otherwise, alpha, beta and sigma2 are initialized by clustering randomly the response Y into K segments.

MStep(statSNMoE, verbose_IRLS)

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