Daniel@0: function path = viterbi_path(prior, transmat, obslik)
Daniel@0: % VITERBI Find the most-probable (Viterbi) path through the HMM state trellis.
Daniel@0: % path = viterbi(prior, transmat, obslik)
Daniel@0: %
Daniel@0: % Inputs:
Daniel@0: % prior(i) = Pr(Q(1) = i)
Daniel@0: % transmat(i,j) = Pr(Q(t+1)=j | Q(t)=i)
Daniel@0: % obslik(i,t) = Pr(y(t) | Q(t)=i)
Daniel@0: %
Daniel@0: % Outputs:
Daniel@0: % path(t) = q(t), where q1 ... qT is the argmax of the above expression.
Daniel@0: 
Daniel@0: 
Daniel@0: % delta(j,t) = prob. of the best sequence of length t-1 and then going to state j, and O(1:t)
Daniel@0: % psi(j,t) = the best predecessor state, given that we ended up in state j at t
Daniel@0: 
Daniel@0: scaled = 1;
Daniel@0: 
Daniel@0: T = size(obslik, 2);
Daniel@0: prior = prior(:);
Daniel@0: Q = length(prior);
Daniel@0: 
Daniel@0: delta = zeros(Q,T);
Daniel@0: psi = zeros(Q,T);
Daniel@0: path = zeros(1,T);
Daniel@0: scale = ones(1,T);
Daniel@0: 
Daniel@0: 
Daniel@0: t=1;
Daniel@0: delta(:,t) = prior .* obslik(:,t);
Daniel@0: if scaled
Daniel@0:   [delta(:,t), n] = normalise(delta(:,t));
Daniel@0:   scale(t) = 1/n;
Daniel@0: end
Daniel@0: psi(:,t) = 0; % arbitrary value, since there is no predecessor to t=1
Daniel@0: for t=2:T
Daniel@0:   for j=1:Q
Daniel@0:     [delta(j,t), psi(j,t)] = max(delta(:,t-1) .* transmat(:,j));
Daniel@0:     delta(j,t) = delta(j,t) * obslik(j,t);
Daniel@0:   end
Daniel@0:   if scaled
Daniel@0:     [delta(:,t), n] = normalise(delta(:,t));
Daniel@0:     scale(t) = 1/n;
Daniel@0:   end
Daniel@0: end
Daniel@0: [p, path(T)] = max(delta(:,T));
Daniel@0: for t=T-1:-1:1
Daniel@0:   path(t) = psi(path(t+1),t+1);
Daniel@0: end
Daniel@0: 
Daniel@0: % If scaled==0, p = prob_path(best_path)
Daniel@0: % If scaled==1, p = Pr(replace sum with max and proceed as in the scaled forwards algo)
Daniel@0: % Both are different from p(data) as computed using the sum-product (forwards) algorithm
Daniel@0: 
Daniel@0: if 0
Daniel@0: if scaled
Daniel@0:   loglik = -sum(log(scale));
Daniel@0:   %loglik = prob_path(prior, transmat, obslik, path);
Daniel@0: else
Daniel@0:   loglik = log(p);
Daniel@0: end
Daniel@0: end