depmixS4 (version 1.5-0)

viterbi: Viterbi algorithm for decoding the most likely state sequence

Description

Apply the Viterbi algorithm to compute the maximum a posteriori state sequence for a mix or depmix object.

Usage

viterbi(object, na.allow=TRUE)

Arguments

object

A mix or depmix object.

na.allow

logical. If TRUE, the density of missing responses is set to 1, similar as in the forwardbackward algorithm. If FALSE, missing values have NA as density values, and will result in an error.

Value

viterbi returns a data.frame with in the first column the maximum a posteriori state sequence. This is a vector with integers corresponding to the index of the most likely hidden states. The remaining columns contain the normalized "delta" probabilities (see Details).

Details

The Viterbi algorithm is used for global decoding of the hidden state sequence. Global decoding is based on the conditional probability \(p(S_1, \ldots, S_T \mid Y_1, \ldots, Y_T)\), and consists of determining, at each time point \(t = 1, \ldots, T\): $$s*_t = \arg \max_{i=1}^N p(S_1 = s*_1, \ldots, S_{t-1} = s*_{t-1}, S_t = i, S_{t+1} = s*_{t+1}, \ldots, S_T = s*_{T} \mid Y_1, \ldots, Y_T)$$ where N is the total number of states.

The Viterbi algorithm is a dynamic programming algorithm that relies on "delta" probabilities (see Rabiner, 1989), which are defined as the joint probability of the most likely state sequence ending in state i at time t, and all the observations up to time t. The implementation here normalizes these probabilities on a time-point basis, dividing the delta probability by the sum of the delta probabilities for that time point for all possible states j (including state i)). The normalized delta probabilities for each state are returned in columns 2:(nstates(object) + 1), whilst column 1 contains the indices of the maximum a posteriori states.

References

Lawrence R. Rabiner (1989). A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of IEEE, 77-2, p. 267-295.

Examples

# NOT RUN {
data(speed)

# 2-state model on rt and corr from speed data set 
# with Pacc as covariate on the transition matrix
# ntimes is used to specify the lengths of 3 separate series
mod <- depmix(list(rt~1,corr~1),data=speed,transition=~Pacc,nstates=2,
	family=list(gaussian(),multinomial("identity")),ntimes=c(168,134,137))
fmod <- fit(mod)
# result of viterbi is stored in a depmix-fitted object in slot "posterior"
identical(viterbi(fmod),fmod@posterior)
# }