# viterbi: Viterbi algorithm for hidden state decoding In RcppHMM: Rcpp Hidden Markov Model

## Description

Function used to get the most likely path of hidden states generated by the observed sequence.

## Usage

 `1` ```viterbi(hmm, sequence) ```

## Arguments

 `hmm` a list with the necessary variables to define a hidden Markov model. `sequence` sequence of observations to be decoded. HMM and PHMM use a vector. GHMM uses a matrix.

## Details

The Viterbi algorithm is based in a greedy approach, therefore it would only the give the most probable path. GHMM uses a matrix with the variables as rows and consecutive observations in the columns.

## Value

A vector with the path of hidden states that generated the observed sequence.

## References

Cited references are listed on the RcppHMM manual page.

`generateObservations` , `verifyModel` , `forwardBackward`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134``` ```## Values for a hidden Markov model with categorical observations # Set the model parameters n <- c("First","Second") m <- c("A","T","C","G") A <- matrix(c(0.8,0.2, 0.1,0.9), nrow = 2, byrow = TRUE) B <- matrix(c(0.2, 0.2, 0.3, 0.3, 0.4, 0.4, 0.1, 0.1), nrow = 2, byrow = TRUE) Pi <- c(0.5, 0.5) params <- list( "Model" = "HMM", "StateNames" = n, "ObservationNames" = m, "A" = A, "B" = B, "Pi" = Pi) HMM <- verifyModel(params) # Data simulation set.seed(100) length <- 100 observationSequence <- generateObservations(HMM, length) #Sequence decoding hiddenStates <- viterbi(HMM, observationSequence\$Y) print(hiddenStates) ## Values for a hidden Markov model with discrete observations n <- c("Low","Normal","High") A <- matrix(c(0.5, 0.3,0.2, 0.2, 0.6, 0.2, 0.1, 0.3, 0.6), ncol=length(n), byrow=TRUE) B <- c(2600, # First distribution with mean 2600 2700, # Second distribution with mean 2700 2800) # Third distribution with mean 2800 Pi <- rep(1/length(n), length(n)) HMM.discrete <- verifyModel(list("Model"="PHMM", "StateNames" = n, "A" = A, "B" = B, "Pi" = Pi)) # Data simulation set.seed(100) length <- 100 observationSequence <- generateObservations(HMM.discrete, length) #Sequence decoding hiddenStates <- viterbi(HMM.discrete, observationSequence\$Y) print(hiddenStates) ## Values for a hidden Markov model with continuous observations # Number of hidden states = 3 # Univariate gaussian mixture model N = c("Low","Normal", "High") A <- matrix(c(0.5, 0.3,0.2, 0.2, 0.6, 0.2, 0.1, 0.3, 0.6), ncol= length(N), byrow = TRUE) Mu <- matrix(c(0, 50, 100), ncol = length(N)) Sigma <- array(c(144, 400, 100), dim = c(1,1,length(N))) Pi <- rep(1/length(N), length(N)) HMM.cont.univariate <- verifyModel(list( "Model"="GHMM", "StateNames" = N, "A" = A, "Mu" = Mu, "Sigma" = Sigma, "Pi" = Pi)) # Data simulation set.seed(100) length <- 100 observationSequence <- generateObservations(HMM.cont.univariate, length) #Sequence decoding hiddenStates <- viterbi(HMM.cont.univariate, observationSequence\$Y) print(hiddenStates) ## Values for a hidden Markov model with continuous observations # Number of hidden states = 2 # Multivariate gaussian mixture model # Observed vector with dimensionality of 3 N = c("X1","X2") M <- 3 # Same number of dimensions Sigma <- array(0, dim =c(M,M,length(N))) Sigma[,,1] <- matrix(c(1.0,0.8,0.8, 0.8,1.0,0.8, 0.8,0.8,1.0), ncol = M, byrow = TRUE) Sigma[,,2] <- matrix(c(1.0,0.4,0.6, 0.4,1.0,0.8, 0.6,0.8,1.0), ncol = M, byrow = TRUE) Mu <- matrix(c(0, 5, 10, 0, 5, 10), nrow = M, byrow = TRUE) A <- matrix(c(0.6, 0.4, 0.3, 0.7), ncol = length(N), byrow = TRUE) Pi <- c(0.5, 0.5) HMM.cont.multi <- verifyModel(list( "Model" = "GHMM", "StateNames" = N, "A" = A, "Mu" = Mu, "Sigma" = Sigma, "Pi" = Pi)) # Data simulation set.seed(100) length <- 100 observationSequence <- generateObservations(HMM.cont.multi, length) #Sequence decoding hiddenStates <- viterbi(HMM.cont.multi, observationSequence\$Y) print(hiddenStates) ```