Viterbi algorithm for state decoding in inhomogeneous HMMs
The Viterbi algorithm allows one to decode the most probable state sequence of an HMM.
viterbi_g(delta, Gamma, allprobs, trackID = NULL, mod = NULL)
delta: initial distribution of length N, or matrix of dimension c(k,N) for k independent tracks, if trackID is provided
Gamma: array of transition probability matrices of dimension c(N,N,n-1), as in a time series of length n, there are only n-1 transitions
If an array of dimension c(N,N,n) is provided for a single track, the first slice will be ignored.
If trackID is provided, Gamma needs to be an array of dimension c(N,N,n), where n is the number of rows in allprobs. Then for each track the first transition matrix will be ignored.
allprobs: matrix of state-dependent probabilities/ density values of dimension c(n, N)
trackID: optional vector of k track IDs, if multiple tracks need to be decoded separately
mod: optional model object containing initial distribution delta, transition probability matrix Gamma, matrix of state-dependent probabilities allprobs, and potentially a trackID variable
If you are using automatic differentiation either with RTMB::MakeADFun or qreml and include forward_g in your likelihood function, the objects needed for state decoding are automatically reported after model fitting. Hence, you can pass the model object obtained from running RTMB::report() or from qreml directly to this function.
vector of decoded states of length n
delta = c(0.5, 0.5) Gamma = array(dim = c(2,2,99)) for(t in 1:99){ gammas = rbeta(2, shape1 = 0.4, shape2 = 1) Gamma[,,t] = matrix(c(1-gammas[1], gammas[1], gammas[2], 1-gammas[2]), nrow = 2, byrow = TRUE) } allprobs = matrix(runif(200), nrow = 100, ncol = 2) states = viterbi_g(delta, Gamma, allprobs)
Other decoding functions: stateprobs(), stateprobs_g(), stateprobs_p(), viterbi(), viterbi_p()