online_em_hmm_demo.m

隐马尔科夫模型对文本信息进行抽取利用MATLAB实现

% Example of online EM


% Generative model
rand('state', 1);
O = 3;
T = 50;
S = 2;
prior0 = normalise(rand(S,1));
transmat0 = mk_stochastic(rand(S,S));
obsmat0 = mk_stochastic(rand(S,O));
data = sample_dhmm(prior0, transmat0, obsmat0, T, 1);


% Initial guess of params
rand('state', 2); % different seed!
transmat1 = mk_stochastic(rand(S,S));
obsmat1 = mk_stochastic(rand(S,O));
prior1 = normalise(rand(S,1));

% Uniformative Dirichlet prior (expected sufficient statistics / pseudo counts)
e = 0.001;
ess_visits = repmat(e, S, 1);
ess_trans = repmat(e, S, S);
ess_emit = repmat(e, S, O);

% Params
w = 2;
decay_sched = [0.1:0.1:0.9];
dirichlet = e;

% Initialize
LL1 = zeros(1,T);
t = 1;
y = data(t);
data_win = y;
[prior1, LL1(1)] = normalise(prior1 .* obsmat1(:,y));

% Iterate
for t=2:T
  y = data(t);
  if t <= w
    data_win = [data_win y];
  else
    data_win = [data_win(2:end) y];
  end
  d = decay_sched(min(t, length(decay_sched)));
  [prior1, transmat1, obsmat1, ess_visits, ess_trans, ess_emit, gamma, ll] = online_em(...
      prior1, transmat1, obsmat1, ess_visits, ess_trans, ess_emit, d, dirichlet, data_win);
  bel = gamma(:, end);
  LL1(t) = ll/length(data_win);
  %fprintf('t=%d, ll=%f\n', t, ll);
end

LL1(1) = LL1(2); % since initial likelihood is for 1 slice
plot(1:T, LL1, 'rx-');

% compare with offline learning

if 0
rand('state', 2);
transmat2 = mk_stochastic(rand(S,S));
obsmat2 = mk_stochastic(rand(S,O));
prior2 = normalise(rand(S,1));
niter = 10;
verbose = 1;
[LL2, prior2, transmat2, obsmat2, gamma] = learn_hmm(data, prior2, transmat2, obsmat2, niter, thresh, verbose);
LL2 = LL2 / T;
end


if 0
% The following approach fails, because doing ML estimation of obsmat based on a short
% window can result in 0s, which cannot be recovered from
niter = 1;
thresh = 1e-2;
verbose = 0;
for t=2:T
  y = data(t);
  if t <= w
    data_win = [data_win y];
  else
    data_win = [data_win(2:end) y];
  end
  [LL, prior1, transmat1, obsmat1, gamma] = learn_hmm(data_win, prior1, transmat1, obsmat1, ...
						  niter, thresh, verbose);
  bel = gamma(:, end);
end
end