wolffd@0: function [prior, transmat] = dbn_to_hmm(bnet)
wolffd@0: % DBN_TO_HMM Compute the discrete HMM matrices from a simple DBN
wolffd@0: % [prior, transmat] = dbn_to_hmm(bnet)
wolffd@0: 
wolffd@0: onodes = bnet.observed;
wolffd@0: ss = length(bnet.intra);
wolffd@0: evidence = cell(1,2*ss);
wolffd@0: hnodes = mysetdiff(1:ss, onodes);
wolffd@0: prior = multiply_CPTs(bnet, [], hnodes, evidence);
wolffd@0: transmat = multiply_CPTs(bnet, hnodes, hnodes+ss, evidence);
wolffd@0: %obsmat1 = multiply_CPTs(bnet, hnodes, onodes, evidence);
wolffd@0: %obsmat = multiply_CPTs(bnet, hnodes+ss, onodes+ss, evidence);
wolffd@0: %obsmat1 = obsmat if the observation matrices are tied across slices
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: %%%%%%%%%%%%
wolffd@0: 
wolffd@0: function mat = multiply_CPTs(bnet, pdom, cdom, evidence)
wolffd@0: 
wolffd@0: % MULTIPLY_CPTS Make a matrix Pr(Y|X), where X represents all the parents, and Y all the children
wolffd@0: % We assume the children have no intra-connections.
wolffd@0: %
wolffd@0: % e.g., Consider the DBN with interconnectivity i->i', j->j',k', k->i',k'
wolffd@0: % Then transition matrix = Pr(i,j,k -> i',j',k') = Pr(i,k->i') Pr(j->j') Pr(j,k->k')
wolffd@0: 
wolffd@0: dom = [pdom cdom];
wolffd@0: ns = bnet.node_sizes;
wolffd@0: bigpot = dpot(dom, ns(dom));
wolffd@0: for j=cdom(:)'
wolffd@0:   e = bnet.equiv_class(j);
wolffd@0:   fam = family(bnet.dag, j);
wolffd@0:   pot = convert_to_pot(bnet.CPD{e}, 'd', fam(:), evidence);
wolffd@0:   bigpot = multiply_by_pot(bigpot, pot);
wolffd@0: end
wolffd@0: psize = prod(ns(pdom));
wolffd@0: csize = prod(ns(cdom));
wolffd@0: T = pot_to_marginal(bigpot);
wolffd@0: mat = reshape(T.T, [psize csize]);
wolffd@0: 
wolffd@0: