ParamMixRHLP-class function

A Reference Class which contains parameters of a mixture of RHLP models.

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

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. $W = (w_{1},\dots,w_{K})$ is an array of dimension $(q + 1, R - 1, K)$, with c("$w_{k} =\n$", "$(w_{k,1},\\dots,w_{k,R-1})$"), $k = 1,\dots,K$, and q the order of the logistic regression. q is fixed to 1 by default.
• beta: Parameters of the polynomial regressions. c("$\\beta =\n$", "$(\\beta_{1},\\dots,\\beta_{K})$") is an array of dimension $(p + 1, R, K)$, with c("$\\beta_{k} =\n$", "$(\\beta_{k,1},\\dots,\\beta_{k,R})$"), $k = 1,\dots,K$, 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).