ParamMixHMM-class function

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

ParamMixHMM contains all the parameters of a mixture of HMM models. class

Fields

• fData: FData object representing the sample (covariates/inputs X and observed responses/outputs Y).
• K: The number of clusters (Number of HMM models).
• R: The number of regimes (HMM components) for each cluster.
• variance_type: Character indicating if the model is homoskedastic (variance_type = "homoskedastic") or heteroskedastic (variance_type = "heteroskedastic"). By default the model is heteroskedastic.
• order_constraint: A logical indicating whether or not a mask of order one should be applied to the transition matrix of the Markov chain to provide ordered states. For the purpose of segmentation, it must be set to TRUE (which is the default value).
• alpha: Cluster weights. Matrix of dimension $(K, 1)$.
• prior: The prior probabilities of the Markov chains. prior is a matrix of dimension $(R, K)$. The k-th column represents the prior distribution of the Markov chain asociated to the cluster k.
• trans_mat: The transition matrices of the Markov chains. trans_mat is an array of dimension $(R, R, K)$.
• mask: Mask applied to the transition matrices trans_mat. By default, a mask of order one is applied.
• mu: Means. Matrix of dimension $(R, K)$. The k-th column gives represents the k-th cluster and gives the means for the R regimes.
• sigma2: The variances for the K clusters. If MixHMM model is heteroskedastic (variance_type = "heteroskedastic") then sigma2 is a matrix of size $(R, K)$ (otherwise MixHMM model is homoskedastic (variance_type = "homoskedastic") and sigma2 is a matrix of size $(1, K)$).
• nu: The degrees of freedom of the MixHMM model representing the complexity of the model.

Methods

• initGaussParamHmm(Y, k, R, variance_type, try_algo): Initialize the means mu and sigma2 for the cluster k.

• initParam(init_kmeans = TRUE, try_algo = 1): Method to initialize parameters alpha, prior, trans_mat, mu and sigma2.

   If `init_kmeans = TRUE` then the curve partition is initialized by the K-means algorithm. Otherwise the curve partition is initialized randomly.
   
   If `try_algo = 1` then `mu` and `sigma2` are initialized by segmenting the time series `Y` uniformly into `R` contiguous segments. Otherwise, `mu` and `sigma2` are initialized by segmenting randomly the time series `Y` into `R` segments.
  

• MStep(statMixHMM): Method which implements the M-step of the EM algorithm to learn the parameters of the MixHMM model based on statistics provided by the object statMixHMM of class StatMixHMM (which contains the E-step).