fixed_lag_smoother.m

隐马尔科夫模型对文本信息进行抽取利用MATLAB实现

function [alpha, gamma, xi] = fixed_lag_smoother(D, alpha, obsmat, transmat, act)
% FIXED_LAG_SMOOTHER
% [alpha, gamma, xi] = fixed_lag_smoother(D, alpha, obsmat, transmat, act) 
%
% D is the delay/lag, so D=0 means online filtering.
% d=min(D+1, t0) is the size of the window we need to keep as history,
% where t0 is the current time.
%
% alpha(:, t0-d-1:t0-1) - length d window, excluding t0 (Columns indexed 1..d)
% obsmat(:, t0-d:t0)    - length d window, last column = likelihood vector for current observation
% transmat            - transition matrix
% If we specify the optional 'act' argument, transmat{a} should be a cell array, and
% act(t0-d:t0)          - length d window, last column = current action
%
% Output:
% alpha(:, t0-d:t0)     - last column = new filtered estimate
% xi(:, :, t0-d:t0-1)   - 2 slice smoothed window
% gamma(:, t0-d:t0)     - smoothed window
%
% As usual, we define (using T=d)
% alpha(i,t) = Pr(Q(t)=i | Y(1:t))
% gamma(i,t) = Pr(Q(t)=i | Y(1:T))
% xi(i,j,t) = Pr(Q(t)=i, Q(t+1)=j | Y(1:T))
%
% obsmat(i,t) = Pr(Y(t) | Q(t)=i) - use mk_dhmm_obs_mat to create this
% transmat{a}(i,j) = Pr(Q(t)=j | Q(t-1)=i, A(t)=a)

[S n] = size(alpha); 

if nargin < 5
  act = ones(1, n+1);
  transmat = { transmat };
end

d = D+1;
d = min(d, n+1); % we can only grow the window to 1 + its current size
d = max(d, 2); % we must always use at least 2 slices
alpha = alpha(:, n-d+2:n); % pluck out last d-1 components

% Extend window by 1
t = d;
xi = zeros(S, S, d-1);
xi(:,:,t-1) = normalise((alpha(:,t-1) * obsmat(:,t)') .* transmat{act(t)});
alpha(:,t) = sum(xi(:,:,t-1), 1)';

% Now smooth backwards inside the window
if D > 0
  beta = ones(S, d);
  T = d;
  gamma(:,T) = alpha(:,T);
  for t=T-1:-1:1
    b = beta(:,t+1) .* obsmat(:,t+1); 
    beta(:,t) = normalise(transmat{act(t)} * b);
    gamma(:,t) = normalise(alpha(:,t) .* beta(:,t));
    xi(:,:,t) = normalise((transmat{act(t)} .* (alpha(:,t) * b')));
  end
end