wehub-resource-sync
38 lines
1.2 KiB
Matlab
Executable File
38 lines
1.2 KiB
Matlab
Executable File
function [gamma, alpha, beta, c] = hmmSmoother(model, x)
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% HMM smoothing alogrithm (normalized forward-backward or normalized alpha-beta algorithm).
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% The alpha and beta returned by this function are the normalized version.
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% Input:
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% x: 1 x n integer vector which is the sequence of observations
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% model: model structure which contains
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% model.s: k x 1 start probability vector
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% model.A: k x k transition matrix
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% model.E: k x d emission matrix
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% Output:
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% gamma: k x n matrix of posterior gamma(t)=p(z_t,x_{1:T})
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% alpha: k x n matrix of posterior alpha(t)=p(z_t|x_{1:T})
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% beta: k x n matrix of posterior beta(t)=gamma(t)/alpha(t)
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% c: 1 x n normalization constant vector
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% Written by Mo Chen (sth4nth@gmail.com).
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s = model.s;
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A = model.A;
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E = model.E;
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n = size(x,2);
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X = sparse(x,1:n,1);
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M = E*X;
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[K,T] = size(M);
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At = A';
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c = zeros(1,T); % normalization constant
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alpha = zeros(K,T);
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[alpha(:,1),c(1)] = normalize(s.*M(:,1),1);
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for t = 2:T
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[alpha(:,t),c(t)] = normalize((At*alpha(:,t-1)).*M(:,t),1); % 13.59
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end
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beta = ones(K,T);
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for t = T-1:-1:1
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beta(:,t) = A*(beta(:,t+1).*M(:,t+1))/c(t+1); % 13.62
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end
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gamma = alpha.*beta; % 13.64
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