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Hidden Markov Model in Julia
module HMM
using Distributions
import Distributions.rand
import Distributions.fit
immutable HiddenMarkovModel{TP, K}
theta::Vector{TP}
A::Matrix{Float64}
pi::Vector{Float64}
function HiddenMarkovModel(theta, A, pi)
assert(length(theta) == K)
assert(size(A) == (K, K))
assert(length(pi) == K)
tol = 1e-6
assert(sum(pi) - 1.0 < tol, sum(pi))
for k=1:K
assert(sum(A[k, :]) - 1.0 < tol, string(k, " ", sum(A[k, :])))
end
return new(theta, A, pi)
end
end
function HiddenMarkovModel{TP}(::Type{TP}, K::Int64)
pi = rand(K)
pi /= sum(pi)
theta = [TP() for k=1:K]
A = rand(K, K)
for k=1:K
A[k, :] /= sum(A[k, :])
end
return HiddenMarkovModel{TP, K}(theta, A, pi)
end
function HiddenMarkovModel{TP}(theta::Vector{TP})
K = length(theta)
pi = rand(K)
pi /= sum(pi)
A = rand(K, K)
for k=1:K
A[k, :] /= sum(A[k, :])
end
return HiddenMarkovModel{TP, K}(theta, A, pi)
end
function rand{TP, K}(hmm::HiddenMarkovModel{TP, K}, len::Int64)
z = zeros(Int, len)
_pi = prior_distribution(hmm)
z[1] = rand(_pi)
_A = transition_distributions(hmm)
for i=2:len
z[i] = rand(_A[z[i-1]])
end
x = Array(typeof(rand(hmm.theta[1])), len)
for i=1:len
x[i] = rand(hmm.theta[z[i]])
end
return (x, z)
end
function transition_distributions{TP, K}(hmm::HiddenMarkovModel{TP, K})
A = Array(Categorical, K)
for k=1:K
A[k, :] = Categorical(vec(hmm.A[k, :]))
end
return A
end
function viterbi{TP, K, TO}(hmm::HiddenMarkovModel{TP, K}, x::Array{TO})
len = length(x)
z = zeros(Int64, len)
backptr = zeros(Int64, len-1, K)
pr = zeros(K)
for k=1:K
pr[k] = logpdf(hmm.theta[k], x[1]) + log(hmm.pi[k])
end
for i=2:len
next_pr = zeros(K)
for k=1:K
maxk, maxp = -1, -Inf
for t=1:K
prob = pr[t] + log(hmm.A[t, k]) + logpdf(hmm.theta[k], x[i])
if prob > maxp
maxk, maxp = t, prob
end
end
backptr[i-1, k] = maxk
next_pr[k] = maxp
end
pr = next_pr
end
z[len] = indmax(pr)
for i=len-1:-1:1
z[i] = backptr[i, z[i+1]]
end
return z
end
numstates{TP, K}(::HiddenMarkovModel{TP, K}) = K
numstates{TP, K}(::Type{HiddenMarkovModel{TP, K}}) = K
partype{TP, K}(::HiddenMarkovModel{TP, K}) = TP
partype{TP, K}(::Type{HiddenMarkovModel{TP, K}}) = TP
function fit{HMM <: HiddenMarkovModel}(hmm_type::Type{HMM}, x; conv_eps=1e-10, init_params=None, fit_param=fit, print_iteration=true)
len = size(x, 1)
K = numstates(hmm_type)
TP = partype(hmm_type)
hmm = if init_params == None
HiddenMarkovModel(TP, K)
else
HiddenMarkovModel(init_params)
end
old_likelihood = -Inf
while true
alpha = zeros(len, K)
beta = zeros(len, K)
c = zeros(len)
alpha[1, :] = hmm.pi .* [pdf(hmm.theta[k], slicedim(x, 1, 1))[1] for k=1:K]
c[1] = sum(alpha[1, :])
alpha[1, :] /= K
for i=2:len
for k=1:K
alpha[i, k] = pdf(hmm.theta[k], slicedim(x, 1, i))[1]
a = 0.
for t=1:K
a += hmm.A[t, k] * alpha[i-1, t]
end
alpha[i, k] *= a
end
c[i] = sum(alpha[i, :])
alpha[i, :] /= c[i]
end
beta[len, :] = 1.
for i=len-1:-1:1
for k=1:K
b = 0.
for t=1:K
b += beta[i+1, t] * pdf(hmm.theta[t], slicedim(x, 1, i+1))[1] * hmm.A[k, t]
end
beta[i, k] = b / c[i+1]
end
end
likelihood = sum(log(c))
if print_iteration == true; println("EM iteration. log-likelihood=", likelihood); end
gamma = alpha .* beta
ksi = zeros(len, K, K)
for i=2:len
for k=1:K
for t=1:K
ksi[i, t, k] = alpha[i-1, t] * beta[i, k] * pdf(hmm.theta[k], slicedim(x, 1, i))[1] * hmm.A[t, k] / c[i]
end
end
end
A = zeros(K, K)
for k=1:K
for t=1:K
for i=2:len
A[k, t] += ksi[i-1, k, t]
end
end
A[k, :] /= sum(A[k, :])
end
theta = Array(TP, 0)
for k=1:K
push!(theta, fit_param(TP, x, vec(gamma[:, k])))
end
hmm = HiddenMarkovModel{TP, K}(theta, A, vec(gamma[1, :] / sum(gamma[1, :])))
#assert(old_likelihood < likelihood, "likelihood should monotonically increase")
if abs(old_likelihood - likelihood) < conv_eps
return hmm
end
old_likelihood = likelihood
end
end
function fit(::Type{Normal}, x::Vector{Float64}, weights::Vector{Float64})
mu = sum(x .* weights) / sum(weights)
y = x - mu
var = sum((y .^ 2) .* weights) / sum(weights)
return Normal(mu, sqrt(var))
end
prior_distribution{TP, K}(hmm::HiddenMarkovModel{TP, K}) = Categorical(hmm.pi)
export HiddenMarkovModel, transition_distributions, prior_distribution, rand
export numstates, partype
export viterbi, fit
end
using HMM
using Distributions
K = 3
theta = [Normal(k, 0.2) for k=1:K]
A = zeros(K, K)
for k=1:K
A[k, :] = 0.1
A[k, k] = 0.8
A[k, :] /= sum(A[k, :])
end
hmm = HiddenMarkovModel{Normal, 3}(theta, A, [0.3, 0.6, 0.1])
#x, z = rand(hmm, 1000)
#est_z = viterbi(hmm, x)
#
#println("Viterbi error:", sum(abs(z - est_z)))
#
#est_hmm = fit(HiddenMarkovModel{Normal, 3}, x)
@zacharyleung

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@zacharyleung

zacharyleung Jul 14, 2015

This looks interesting but I am not sure what the code does. Could you please briefly describe what kind of hidden Markov model this code is estimating?

This looks interesting but I am not sure what the code does. Could you please briefly describe what kind of hidden Markov model this code is estimating?

@brice-olivier

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brice-olivier Sep 11, 2017

If some people are still wondering after all that time... As far as I understood, this is a monosequence HMM with a univariate Gaussian output process.

If some people are still wondering after all that time... As far as I understood, this is a monosequence HMM with a univariate Gaussian output process.

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