matthiasm@43: function path = viterbi_path(prior, transmat, obslik)
matthiasm@43: % VITERBI Find the most-probable (Viterbi) path through the HMM state trellis.
matthiasm@43: % path = viterbi(prior, transmat, obslik)
matthiasm@43: %
matthiasm@43: % Inputs:
matthiasm@43: % prior(i) = Pr(Q(1) = i)
matthiasm@43: % transmat(i,j) = Pr(Q(t+1)=j | Q(t)=i)
matthiasm@43: % obslik(i,t) = Pr(y(t) | Q(t)=i)
matthiasm@43: %
matthiasm@43: % Outputs:
matthiasm@43: % path(t) = q(t), where q1 ... qT is the argmax of the above expression.
matthiasm@43: 
matthiasm@43: 
matthiasm@43: % delta(j,t) = prob. of the best sequence of length t-1 and then going to state j, and O(1:t)
matthiasm@43: % psi(j,t) = the best predecessor state, given that we ended up in state j at t
matthiasm@43: 
matthiasm@43: scaled = 1;
matthiasm@43: 
matthiasm@43: T = size(obslik, 2);
matthiasm@43: prior = prior(:);
matthiasm@43: Q = length(prior);
matthiasm@43: 
matthiasm@43: delta = zeros(Q,T);
matthiasm@43: psi = zeros(Q,T);
matthiasm@43: path = zeros(1,T);
matthiasm@43: scale = ones(1,T);
matthiasm@43: 
matthiasm@43: 
matthiasm@43: t=1;
matthiasm@43: delta(:,t) = prior .* obslik(:,t);
matthiasm@43: if scaled
matthiasm@43:   [delta(:,t), n] = normalise(delta(:,t));
matthiasm@43:   scale(t) = 1/n;
matthiasm@43: end
matthiasm@43: psi(:,t) = 0; % arbitrary value, since there is no predecessor to t=1
matthiasm@43: for t=2:T
matthiasm@43:   for j=1:Q
matthiasm@43:     [delta(j,t), psi(j,t)] = max(delta(:,t-1) .* transmat(:,j));
matthiasm@43:     delta(j,t) = delta(j,t) * obslik(j,t);
matthiasm@43:   end
matthiasm@43:   if scaled
matthiasm@43:     [delta(:,t), n] = normalise(delta(:,t));
matthiasm@43:     scale(t) = 1/n;
matthiasm@43:   end
matthiasm@43: end
matthiasm@43: [p, path(T)] = max(delta(:,T));
matthiasm@43: for t=T-1:-1:1
matthiasm@43:   path(t) = psi(path(t+1),t+1);
matthiasm@43: end
matthiasm@43: 
matthiasm@43: % If scaled==0, p = prob_path(best_path)
matthiasm@43: % If scaled==1, p = Pr(replace sum with max and proceed as in the scaled forwards algo)
matthiasm@43: % Both are different from p(data) as computed using the sum-product (forwards) algorithm
matthiasm@43: 
matthiasm@43: if 0
matthiasm@43: if scaled
matthiasm@43:   loglik = -sum(log(scale));
matthiasm@43:   %loglik = prob_path(prior, transmat, obslik, path);
matthiasm@43: else
matthiasm@43:   loglik = log(p);
matthiasm@43: end
matthiasm@43: end