emMixHMM {flamingos}

emMixHMM implemens the EM (Baum-Welch) algorithm to fit a mixture of HMM models.

Description

emMixHMM implements the maximum-likelihood parameter estimation of a mixture of HMM models by the Expectation-Maximization (EM) algorithm, known as Baum-Welch algorithm in the context of mixHMM.

Usage

emMixHMM(Y, K, R, variance_type = c("heteroskedastic", "homoskedastic"),
  order_constraint = TRUE, init_kmeans = TRUE, n_tries = 1,
  max_iter = 1000, threshold = 1e-06, verbose = FALSE)

Arguments

Y

Matrix of size (n, m) representing the observed responses/outputs. Y consists of n functions of X observed at points 1,\dots,m.

K

The number of clusters (Number of HMM models).

R

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

variance_type

Optional character indicating if the model is "homoskedastic" or "heteroskedastic". By default the model is "heteroskedastic".

order_constraint

Optional. 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).

init_kmeans

Optional. A logical indicating whether or not the curve partition should be initialized by the K-means algorithm. Otherwise the curve partition is initialized randomly.

n_tries

Optional. Number of runs of the EM algorithm. The solution providing the highest log-likelihood will be returned.

If n_tries > 1, then for the first run, parameters are initialized by uniformly segmenting the data into K segments, and for the next runs, parameters are initialized by randomly segmenting the data into K contiguous segments.

max_iter

Optional. The maximum number of iterations for the EM algorithm.

threshold

Optional. A numeric value specifying the threshold for the relative difference of log-likelihood between two steps of the EM as stopping criteria.

verbose

Optional. A logical value indicating whether or not values of the log-likelihood should be printed during EM iterations.

Details

emMixHMM function implements the EM algorithm. This function starts with an initialization of the parameters done by the method initParam of the class ParamMixHMM, then it alternates between the E-Step (method of the class StatMixHMM) and the M-Step (method of the class ParamMixHMM) until convergence (until the relative variation of log-likelihood between two steps of the EM algorithm is less than the threshold parameter).

Value

EM returns an object of class ModelMixHMM.

See Also

ModelMixHMM, ParamMixHMM, StatMixHMM

Examples

data(toydataset)
Y <- t(toydataset[,2:ncol(toydataset)])

mixhmm <- emMixHMM(Y = Y, K = 3, R = 3, verbose = TRUE)

mixhmm$summary()

mixhmm$plot()