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基于matlab的HMM源代码

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本程序是基于matlab环境下的隐马尔科夫模型（HMM）源程序代码非常适合初学者的学习和研究

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一下是 HMM 的代码

dhmm_em.m

function [LL, prior, transmat, obsmat, nrIterations] = ...

dhmm_em(data, prior, transmat, obsmat, varargin)

% LEARN_DHMM Find the ML/MAP parameters of an HMM with discrete outputs using

EM.

% [ll_trace, prior, transmat, obsmat, iterNr] = learn_dhmm(data, prior0, transmat0,

obsmat0, ...)

% Notation: Q(t) = hidden state, Y(t) = observation

% INPUTS:

% data{ex} or data(ex,:) if all sequences have the same length

% prior(i)

% transmat(i,j)

% obsmat(i,o)

% Optional parameters may be passed as 'param_name', param_value pairs.

% Parameter names are shown below; default values in [] - if none, argument is

mandatory.

% 'max_iter' - max number of EM iterations [10]

% 'thresh' - convergence threshold [1e-4]

% 'verbose' - if 1, print out loglik at every iteration [1]

% 'obs_prior_weight' - weight to apply to uniform dirichlet prior on observation matrix [0]

% To clamp some of the parameters, so learning does not change them:

% 'adj_prior' - if 0, do not change prior [1]

% 'adj_trans' - if 0, do not change transmat [1]

% 'adj_obs' - if 0, do not change obsmat [1]

% Modified by Herbert Jaeger so xi are not computed individually

% but only their sum (over time) as xi_summed; this is the only way how they are used

% and it saves a lot of memory.

[max_iter, thresh, verbose, obs_prior_weight, adj_prior, adj_trans, adj_obs] = ...

process_options(varargin, 'max_iter', 10, 'thresh', 1e-4, 'verbose', 1, ...

'obs_prior_weight', 0, 'adj_prior', 1, 'adj_trans', 1, 'adj_obs', 1);

previous_loglik = -inf;

loglik = 0;

converged = 0;

num_iter = 1;

LL = [];

if ~iscell(data)

data = num2cell(data, 2); % each row gets its own cell

end

while (num_iter <= max_iter) & ~converged

% E step

[loglik, exp_num_trans, exp_num_visits1, exp_num_emit] = ...

compute_ess_dhmm(prior, transmat, obsmat, data, obs_prior_weight);

% M step

if adj_prior

prior = normalise(exp_num_visits1);

end

if adj_trans & ~isempty(exp_num_trans)

transmat = mk_stochastic(exp_num_trans);

end

if adj_obs

obsmat = mk_stochastic(exp_num_emit);

end

if verbose, fprintf(1, 'iteration %d, loglik = %f/n', num_iter, loglik); end

num_iter = num_iter + 1;

converged = em_converged(loglik, previous_loglik, thresh);

previous_loglik = loglik;

LL = [LL loglik];

end

nrIterations = num_iter - 1;

%%%%%%%%%%%%%%%%%%%%%%%

function [loglik, exp_num_trans, exp_num_visits1, exp_num_emit, exp_num_visitsT] = ...

compute_ess_dhmm(startprob, transmat, obsmat, data, dirichlet)

% COMPUTE_ESS_DHMM Compute the Expected Sufficient Statistics for an HMM with

discrete outputs

% function [loglik, exp_num_trans, exp_num_visits1, exp_num_emit, exp_num_visitsT] =

...

% compute_ess_dhmm(startprob, transmat, obsmat, data, dirichlet)

% INPUTS:

% startprob(i)

% transmat(i,j)

% obsmat(i,o)

% data{seq}(t)

% dirichlet - weighting term for uniform dirichlet prior on expected emissions

% OUTPUTS:

% exp_num_trans(i,j) = sum_l sum_{t=2}^T Pr(X(t-1) = i, X(t) = j| Obs(l))

% exp_num_visits1(i) = sum_l Pr(X(1)=i | Obs(l))

% exp_num_visitsT(i) = sum_l Pr(X(T)=i | Obs(l))

% exp_num_emit(i,o) = sum_l sum_{t=1}^T Pr(X(t) = i, O(t)=o| Obs(l))

% where Obs(l) = O_1 .. O_T for sequence l.

numex = length(data);

[S O] = size(obsmat);

exp_num_trans = zeros(S,S);

exp_num_visits1 = zeros(S,1);

exp_num_visitsT = zeros(S,1);

exp_num_emit = dirichlet*ones(S,O);

loglik = 0;

for ex=1:numex

obs = data{ex};

T = length(obs);

%obslik = eval_pdf_cond_multinomial(obs, obsmat);

obslik = multinomial_prob(obs, obsmat);

[alpha, beta, gamma, current_ll, xi_summed] = fwdback(startprob, transmat, obslik);

loglik = loglik + current_ll;

exp_num_trans = exp_num_trans + xi_summed;

exp_num_visits1 = exp_num_visits1 + gamma(:,1);

exp_num_visitsT = exp_num_visitsT + gamma(:,T);

% loop over whichever is shorter

if T < O

for t=1:T

o = obs(t);

exp_num_emit(:,o) = exp_num_emit(:,o) + gamma(:,t);

end

else

for o=1:O

ndx = find(obs==o);

if ~isempty(ndx)

exp_num_emit(:,o) = exp_num_emit(:,o) + sum(gamma(:, ndx), 2);

end

--------

dhmm_logprob.m

--------

function [loglik, errors] = dhmm_logprob(data, prior, transmat, obsmat)

% LOG_LIK_DHMM Compute the log-likelihood of a dataset using a discrete HMM

% [loglik, errors] = log_lik_dhmm(data, prior, transmat, obsmat)

% data{m} or data(m,:) is the m'th sequence

% errors is a list of the cases which received a loglik of -infinity

if ~iscell(data)

data = num2cell(data, 2);

end

ncases = length(data);

loglik = 0;

errors = [];

for m=1:ncases

obslik = multinomial_prob(data{m}, obsmat);

[alpha, beta, gamma, ll] = fwdback(prior, transmat, obslik, 'fwd_only', 1);

if ll==-inf

errors = [errors m];

end

loglik = loglik + ll;

end

-------

em_converged.m

-------

function [converged, decrease] = em_converged(loglik, previous_loglik, threshold)

% EM_CONVERGED Has EM converged?

% [converged, decrease] = em_converged(loglik, previous_loglik, threshold)

% We have converged if

% |f(t) - f(t-1)| / avg < threshold,

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大牛解庖丁

2013-06-06

一般，看不懂，有点乱，注释不详细

基于matlab的HMM源代码

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