wolffd@0: function [transprob, termprob] = remove_hhmm_end_state(A)
wolffd@0: % REMOVE_END_STATE Infer transition and termination probabilities from automaton with an end state
wolffd@0: % [transprob, termprob] = remove_end_state(A)
wolffd@0: %
wolffd@0: % A(i,k,j) = Pr( i->j | Qps=k), where i in 1:Q, j in 1:(Q+1), and Q+1 is the end state
wolffd@0: % This implements the equation in footnote 3 of my NIPS 01 paper,
wolffd@0: % transprob(i,k,j) = \tilde{A}_k(i,j)
wolffd@0: % termprob(k,j) = \tau_k(j)
wolffd@0: %
wolffd@0: % For the top level, the k index is missing.
wolffd@0: 
wolffd@0: Q = size(A,1);
wolffd@0: toplevel = (ndims(A)==2);
wolffd@0: if toplevel
wolffd@0:   Qk = 1;
wolffd@0:   A = reshape(A, [Q 1 Q+1]);
wolffd@0: else
wolffd@0:   Qk = size(A, 2);
wolffd@0: end
wolffd@0: 
wolffd@0: transprob = A(:, :, 1:Q);
wolffd@0: term = A(:,:,Q+1)'; % term(k,j) = P(Qj -> end | k)
wolffd@0: termprob = term;
wolffd@0: %termprob = zeros(Qk, Q, 2);
wolffd@0: %termprob(:,:,2) = term;
wolffd@0: %termprob(:,:,1) = 1-term;
wolffd@0: 
wolffd@0: for k=1:Qk
wolffd@0:   for i=1:Q
wolffd@0:     for j=1:Q
wolffd@0:       denom = (1-termprob(k,i));
wolffd@0:       denom = denom + (denom==0)*eps;
wolffd@0:       transprob(i,k,j) = transprob(i,k,j) / denom;
wolffd@0:     end
wolffd@0:   end    
wolffd@0: end
wolffd@0: 
wolffd@0: if toplevel
wolffd@0:   termprob = squeeze(termprob);
wolffd@0:   transprob = squeeze(transprob);
wolffd@0: end