learn_dhmm_simple.m

上载文件为Matlab环境下的高斯以马尔科夫模型例程

function [hmm, LL] = learn_dhmm_simple(data, hmm, varargin)
% LEARN_DHMM_SIMPLE Find the ML/MAP params of an HMM with discrete outputs using EM 
%
% [hmm, LL] = learn_dhmm_simple(data, hmm, ...)
%
% Input
%   data{m} is the m'th training sequence.
%   hmm is a structure created with mk_rnd_dhmm.
%
% Output
%   hmm is a structure containing the learned params
%   LL(i) is the log likelihood at iteration i
%
% Optional arguments are passed as name/value pairs, e.g, 
%    learn_dhmm(data, hmm, 'max_iter', 30)
% Defaults are in [brackets]
%
% max_iter - max num iterations [100]
% thresh - threshold for stopping EM (relative change in log-lik must drop below this) [1e-4]
% verbose - 1 means display the log lik at each iteration [0]
% dirichlet - equivalent sample size of a uniform Dirichlet prior applied to obsmat [0]
%
% anneal - do deterministic annealing? [0]
% anneal_fully - force temperature to go all the way to 0? [0]
% anneal_rate - rate at which inverse temperature is increased (should be between 1.1 and 1.5) [1.2]
% init_beta - initial inverse temperature (should be between 0.01 and 0.5) [0.1]

max_iter = 100;
thresh = 1e-4;
verbose = 0;
dirichlet = 0;
anneal = 0;
anneal_fully = 0;
anneal_rate = 1.2;
init_beta = 0.1;

if nargin >= 3
  args = varargin;
  for i=1:2:length(args)
    switch args{i},
     case 'max_iter', max_iter = args{i+1};
     case 'thresh', thresh = args{i+1};
     case 'verbose', verbose = args{i+1};
     case 'dirichlet', dirichlet = args{i+1};
     case 'anneal', anneal = args{i+1};
     case 'anneal_rate', anneal_rate = args{i+1};
     case 'anneal_fully', anneal_fully = args{i+1};
     case 'init_beta', init_beta = args{i+1};
    end
  end
end      


if anneal
  % schedule taken from Ueda and Nakano, "Determinsitic Annealing EM algorithm",
  % Neural Networks 11 (1998): 271-282, p276
  b = [];
  temp = [];
  i = 1;
  b(i)=init_beta;
  temp(i)=1/b(i);
  while b(i) < 1
    i = i + 1;
    b(i)=b(i-1)*anneal_rate;
    temp(i)=1/b(i);
  end
  temp_schedule = temp;
end

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
numex = length(data);

startprob = hmm.startprob;
endprob = hmm.endprob;
transmat = hmm.transmat;
obsmat = hmm.obsmat;

while (num_iter <= max_iter) & ~converged
  if anneal & num_iter <= length(temp_schedule)
    temp = temp_schedule(num_iter);
  else
    temp = 1;
  end
  
  % E step
  [loglik, exp_num_trans, exp_num_visits1, exp_num_emit, exp_num_visitsT] = ...
      compute_ess_dhmm(startprob, transmat, obsmat, data, dirichlet, temp);

  if verbose
    if anneal
      fprintf(1, 'iteration %d, loglik = %f, temp = %5.3f\n', num_iter, loglik, temp);
    else
      fprintf(1, 'iteration %d, loglik = %f\n', num_iter, loglik);
    end
  end
  num_iter =  num_iter + 1;

  % M step
  startprob = normalise(exp_num_visits1);
  endprob = normalise(exp_num_visitsT );
  obsmat = mk_stochastic(exp_num_emit);
  transmat = mk_stochastic(exp_num_trans);
  
  converged = em_converged(loglik, previous_loglik, thresh);
  if anneal_fully
    % must cool all the way and do at least 3 steps at temp=1 before finishing
    if num_iter <= length(temp_schedule)+3
      converged = 0;
    end
  end

  previous_loglik = loglik;
  LL = [LL loglik];
end

hmm.startprob = startprob;
hmm.endprob = endprob;
hmm.transmat = transmat;
hmm.obsmat = obsmat;