viterbi: Most probable state sequence.

In hmm.discnp: Hidden Markov Models with Discrete Non-Parametric Observation Distributions

Most probable state sequence.

Description

Calculates “the” most probable state sequence underlying each of one or more replicate observation sequences.

Usage

viterbi(y, model = NULL, tpm, Rho, ispd=NULL,log=FALSE, warn=TRUE)

Arguments

y	The observations for which the most probable sequence(s) of underlying hidden states are required. May be a sequence of observations in the form of a vector or a one or two column matrix, or a list each component of which constitutes a (replicate) sequence of observations. It may also be an object of class "multipleHmmDataSets" as returned by rhmm() with nsim>1. If y is missing, it is extracted from model (whence it will not be of class "multipleHmmDataSets"!) provided that model and its y component are not NULL. Otherwise an error is given.
model	An object describing a hidden Markov model, as fitted to the data set y by hmm().
tpm	The transition probability matrix for a hidden Markov model; ignored if model is non-null.
Rho	An object specifying the probability distributions of the observations for a hidden Markov model. See hmm(). Ignored if model is non-null. Should bear some reasonable relationship to y. If Rho has dimension names (or if its entries have dimension names in the case where Rho is a list) then the appropriate dimension names must include all corresponding values of the observations. If a relevant vector of dimension names is NULL then it is formed as the sort unique values of the approprate columns of the observation matrices. In this case the corresponding dimensions must match the number of unique values.
ispd	The initial state probability distribution for a hidden Markov model; ignored if model is non-null. Should bear some reasonable relationship to y. If model and ispd are both NULL then ispd is set equal to the stationary distribution calculated from tpm.
log	Logical scalar. Should logarithms be used in the recursive calculations of the probabilities involved in the Viterbi algorithm, so as to avoid underflow? If log is FALSE then underflow is avoided instead by a normalization procedure. The quantity delta (see Rabiner 1989, page 264) is replaced by delta/sum(delta) at each step. It should actually make no difference whether log is set to TRUE. I just included the option because I could. Also the HMM package uses the logarithm approach so setting log=TRUE might be of interest if comparisons are to be made between results from the two packages.
warn	Logical scalar; should a warning be issued if Rho hasn't got relevant dimension names? (Note that if this is so, then the corresponding dimension names are formed from the sorted unique values of y or of the appropriate column(s) of y. And if this is so, then the user should be sure that the ordering of the entries of Rho corresponds properly to the the sorted unique values of y.) This argument is passed to the utility function check.yval() which actually issues the warning if warn=TRUE.

Details

Applies the Viterbi algorithm to calculate “the” most probable robable state sequence underlying each observation sequences.

Value

If y consists of a single observation sequence, the value is the underlying most probable observation sequence, or a matrix whose columns consist of such sequences if there is more than one (equally) most probable sequence.

If y consists of a list of observation sequences, the value is a list each entry of which is of the form described above.

If y is of class "multipleHmmDataSets" then the value returned is a list of lists of the sort described above.

Warning

There may be more than one equally most probable state sequence underlying a given observation sequence. This phenomenon can occur but appears to be unlikely to do so in practice.

Thanks

The correction made to the code so as to avoid underflow problems was made due to an inquiry and suggestion from Owen Marshall.

Author(s)

Rolf Turner [e-mail]

References

Rabiner, L. R., "A tutorial on hidden Markov models and selected applications in speech recognition," Proc. IEEE vol. 77, pp. 257 – 286, 1989.

See Also

hmm(), rhmm(), mps(), pr()

Examples

# See the help for logLikHmm() for how to generate y.num and y.let.
## Not run: 
fit.num     <- hmm(y.num,K=2,verb=TRUE,keep.y=TRUE)
v.1         <- viterbi(model=fit.num)
rownames(R) <- 1:5 # Avoids a (harmless) warning.
v.2         <- viterbi(y.num,tpm=P,Rho=R)
# P and R as in the help for logLikHmm() and for sp().

# Note that the order of the states has gotten swapped; 3-v.1[[1]]
# is identical to v.2[[1]]; for other k = 2, ..., 20, 3-v.1[[k]]
# is much more similar to v.2[[k]] than is v.1[[k]].

fit.let <- hmm(y.let,K=2,verb=TRUE,keep.y=TRUE))
v.3 <- viterbi(model=fit.let)
rownames(R) <- letters[1:5]
v.4 <- viterbi(y.let,tpm=P,Rho=R)

## End(Not run)

hmm.discnp documentation built on Sept. 26, 2022, 5:05 p.m.