Note: There is now a registered package HiddenMarkovModels.jl. This package is no longer maintained (but it still works).

HiddenMarkovModel.jl

This is an old module for fitting Hidden Markov Models in Julia. Also check out ToyHMM.jl, for a simple implementation of a discrete HMM in Julia.

Installation

The package is not registered (yet), so to download the code use:

Pkg.clone("https://github.com/ahwillia/HiddenMarkovModel.jl")

Example HMM with Gaussian Emissions

The code below creates two Hidden Markov Models: hmm and hmm_true. A dataset is generated from hmm_true and parameters for hmm are fit based on this dataset, and are shown to resemble the ground truth (i.e. the parameters of hmm_true).

using HiddenMarkovModel
using Distributions

# Creates a Gaussian HMM with 2 hidden states (default params)
hmm = HMM(2,Normal()) 

## Create some synthetic training data
μ1,μ2 = -20,15 # mean emission of state 1 and state 2
σ1,σ2 = 3,5    # std of emissions in state 1 and state 2

# A is the transition matrix, B is an Array of emission Distributions
A = [ 0.9 0.1 ; 0.8 0.2 ]
B = (Distribution)[ Normal(μ1,σ1) , Normal(μ2,σ2) ]

# Create the HMM and draw 10 thousand samples from it
hmm_true = HMM(A,B)
s,o = generate(hmm_true,10_000)

# s is a vector of integers specifying the hidden states
# o is a vector of floats specifying the observations

# Use Baum-Welch algorithm to fit the parameters of our first
# HMM object (with default parameters) to the synthetic dataset
ll = fit!(hmm,o)

# ll is the log-likelihood at each iteration.

The fit! command modifies the hmm parameters to fit the observations, o. Different datasets and random initializations will produce different solutions, but typical results are shown below:

julia> hmm.A
2x2 Array{Float64,2}:
 0.212806   0.787194
 0.0994928  0.900507

julia> hmm.B[1]
Normal(μ=14.871948267720121, σ=5.065092399554946)

julia> hmm.B[2]
Normal(μ=-20.05831728323262, σ=3.007059450241878)