viterbi: Most probable state sequence. In hmm.discnp: Hidden Markov Models with Discrete Non-Parametric Observation Distributions

Description

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

Usage

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

Arguments

 `y` The observations for which the underlying most probable hidden states are required. May be a sequence of observations, or a list each entry of which constitutes an independent sequence of observations. If `y` is missing (and if `model` is not `NULL`) then `y` is extracted from `model`, provided that the `y` component of `model` is present. 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 the results of 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.

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 [email protected]

References

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

`hmm()`, `rhmm()`, `mps()`, `pr()`, `viterbi()`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```# See the help for rhmm() for how to generate y.num and y.let. ## Not run: fit.num <- hmm(y.num,K=2,verb=TRUE) v.1 <- viterbi(model=fit.num) v.2 <- viterbi(y.num,tpm=P,Rho=R) # P and R as in the # help for rhmm(). # The order of the states has gotten swapped; 3-v.1[[1]] is much # more similar to v.2[[1]] than is v.1[[1]]. fit.let <- hmm(y.let,K=2,verb=TRUE) v.3 <- viterbi(model=fit.let) # Works. v.4 <- viterbi(y.let,tpm=P,Rho=R) # Throws an error (R has no row names.) ## End(Not run) ```