example1.m

隐马尔科夫模型对文本信息进行抽取利用MATLAB实现

% Example of fixed lag smoothing

S = 2;
O = 2;
T = 5;
data = sample_discrete([0.5 0.5], 1, T);
transmat = mk_stochastic(rand(S,S));
obsmat = mk_stochastic(rand(S,O));
B = mk_dhmm_obs_mat(data, obsmat);
prior = [0.5 0.5]';

% window width 2, i.e., filtering

alpha0 = forwards(prior, transmat, B);

w = 2;
alpha1 = zeros(S, T);
t = 1;
alpha1(:,t) = normalise(prior .* B(:,t));
for t=2:T
  [alpha1(:,t-1:t), gamma1(:,t-1:t), xi1(:,:,t-1)] = fixed_lag_smoother(w, alpha1(:,t-1), B(:,t-1:t), transmat);
end

assert(approxeq(alpha0, alpha1));



% lag 1

[alpha0, beta0, gamma0, xi0] = forwards_backwards(prior, transmat, B);

D = 1;
alpha1 = zeros(S, T);
t = 1;
alpha1(:,t) = normalise(prior .* B(:,t));
for t=2:T
  [alpha1(:,t-1:t), gamma1(:,t-1:t), xi1(:,:,t-1)] = fixed_lag_smoother(D, alpha1(:,t-1), B(:,t-1:t), transmat);
end


w = 3;
alpha1 = zeros(S, T);
gamma1 = zeros(S, T);
xi1 = zeros(S, S, T-1);
t = 1;
y = data(t);
b = obsmat(:, y);
bwindow = b;
alpha_window = normalise(prior .* b);
alpha1(:,t) = alpha_window;
for t=2:w
  y = data(t);
  b = obsmat(:, y);
  bwindow = [bwindow b];
  [alpha_window, gamma_window, xi_window] = fixed_lag_smoother(w, alpha_window, bwindow, transmat);
  alpha1(:,1:t) = alpha_window;
  gamma1(:,1:t) = gamma_window;
  xi1(:,:,1:t-1) = xi_window;    
end
for t=w+1:T
  y = data(t);
  b = obsmat(:, y);
  bwindow = [bwindow(:,2:end) b];
  [alpha_window, gamma_window, xi_window] = fixed_lag_smoother(D, alpha_window(:,2:end), bwindow, transmat);
  alpha1(:,t-D:t) = alpha_window;
  gamma1(:,t-D:t) = gamma_window;
  xi1(:,:,t-D:t-1) = xi_window;    
end