Algorithms

fit_mle(hmm, observations; ...) -> AbstractHMM

Estimate the HMM parameters using the EM (Baum-Welch) algorithm, with hmm as the initial state.

Keyword Arguments

• display::Symbol = :none: when to display convergence logs, can be set to :iter or :final.
• init::Symbol = :none: if set to :kmeans the HMM parameters will be initialized using a K-means clustering.
• maxiter::Integer = 100: maximum number of iterations to perform.
• tol::Integer = 1e-3: stop the algorithm when the improvement in the log-likelihood is less than tol.

Output

• <:AbstractHMM: a copy of the original HMM with the updated parameters.

forward(a, A, L; logl) -> (Vector, Float)

Compute forward probabilities using samples likelihoods. See Forward-backward algorithm.

Output

• Vector{Float64}: forward probabilities.
• Float64: log-likelihood of the observed sequence.

forward(hmm, observations; logl, robust) -> (Vector, Float)

Compute forward probabilities of the observations given the hmm model.

Output

• Vector{Float64}: forward probabilities.
• Float64: log-likelihood of the observed sequence.

Example

using Distributions, HMMBase
hmm = HMM([0.9 0.1; 0.1 0.9], [Normal(0,1), Normal(10,1)])
y = rand(hmm, 1000)
probs, tot = forward(hmm, y)

backward(a, A, L; logl) -> (Vector, Float)

Compute backward probabilities using samples likelihoods. See Forward-backward algorithm.

Output

• Vector{Float64}: backward probabilities.
• Float64: log-likelihood of the observed sequence.

backward(hmm, observations; logl, robust) -> (Vector, Float)

Compute backward probabilities of the observations given the hmm model.

Output

• Vector{Float64}: backward probabilities.
• Float64: log-likelihood of the observed sequence.

Example

using Distributions, HMMBase
hmm = HMM([0.9 0.1; 0.1 0.9], [Normal(0,1), Normal(10,1)])
y = rand(hmm, 1000)
probs, tot = backward(hmm, y)

posteriors(α, β) -> Vector

Compute posterior probabilities from α and β.

Arguments

• α::AbstractVector: forward probabilities.
• β::AbstractVector: backward probabilities.

posteriors(a, A, L; logl) -> Vector

Compute posterior probabilities using samples likelihoods.

posteriors(hmm, observations; logl, robust) -> Vector

Compute posterior probabilities using samples likelihoods.

Example

using Distributions, HMMBase
hmm = HMM([0.9 0.1; 0.1 0.9], [Normal(0,1), Normal(10,1)])
y = rand(hmm, 1000)
γ = posteriors(hmm, y)

viterbi(a, A, L; logl) -> Vector

Find the most likely hidden state sequence, see Viterbi algorithm.

viterbi(hmm, observations; logl, robust) -> Vector

Example

using Distributions, HMMBase
hmm = HMM([0.9 0.1; 0.1 0.9], [Normal(0,1), Normal(10,1)])
y = rand(hmm, 1000)
zv = viterbi(hmm, y)