wolffd@0: % make a factor graph corresponding to an  HMM, where we absorb the evidence up front,
wolffd@0: % and then eliminate the observed nodes.
wolffd@0: % Compare this with not absorbing the evidence.
wolffd@0: 
wolffd@0: seed = 1;
wolffd@0: rand('state', seed);
wolffd@0: randn('state', seed);
wolffd@0: 
wolffd@0: T = 3;
wolffd@0: Q = 3;
wolffd@0: O = 2;
wolffd@0: cts_obs = 0;
wolffd@0: param_tying = 1;
wolffd@0: bnet = mk_hmm_bnet(T, Q, O, cts_obs, param_tying);
wolffd@0: N = 2*T;
wolffd@0: onodes = bnet.observed;
wolffd@0: hnodes = mysetdiff(1:N, onodes);
wolffd@0: 
wolffd@0: data = sample_bnet(bnet);
wolffd@0: 
wolffd@0: init_factor = bnet.CPD{1};
wolffd@0: obs_factor = bnet.CPD{3};
wolffd@0: edge_factor = bnet.CPD{2}; % trans matrix
wolffd@0: 
wolffd@0: nfactors = T;
wolffd@0: nvars = T; % hidden only
wolffd@0: G = zeros(nvars, nfactors);
wolffd@0: G(1,1) = 1;
wolffd@0: for t=1:T-1
wolffd@0:   G(t:t+1, t+1)=1;
wolffd@0: end
wolffd@0: 
wolffd@0: node_sizes = Q*ones(1,T);
wolffd@0: 
wolffd@0: % We tie params as follows:
wolffd@0: % the first hidden node use init_factor (number 1)
wolffd@0: % all hidden nodes on the backbone use edge_factor (number 2)
wolffd@0: % all observed nodes use the same factor, namely obs_factor
wolffd@0: 
wolffd@0: small_fg = mk_fgraph_given_ev(G, node_sizes, {init_factor, edge_factor}, {obs_factor}, data(onodes), ...
wolffd@0: 			 'equiv_class', [1 2*ones(1,T-1)], 'ev_equiv_class', ones(1,T));
wolffd@0: 
wolffd@0: small_bnet = fgraph_to_bnet(small_fg);
wolffd@0: 
wolffd@0: % don't pre-process evidence
wolffd@0: big_fg = bnet_to_fgraph(bnet);
wolffd@0: big_bnet = fgraph_to_bnet(big_fg);
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: engine = {};
wolffd@0: engine{1} = jtree_inf_engine(bnet);
wolffd@0: engine{2} = belprop_fg_inf_engine(small_fg, 'max_iter', 2*T);
wolffd@0: engine{3} = jtree_inf_engine(small_bnet);
wolffd@0: engine{4} = belprop_fg_inf_engine(big_fg, 'max_iter', 3*T);
wolffd@0: engine{5} = jtree_inf_engine(big_bnet);
wolffd@0: nengines = length(engine);
wolffd@0: 
wolffd@0: 
wolffd@0: % on BN, use the original evidence
wolffd@0: evidence = cell(1, 2*T);
wolffd@0: evidence(onodes) = data(onodes);
wolffd@0: tic; [engine{1}, ll(1)] = enter_evidence(engine{1}, evidence); toc
wolffd@0: 
wolffd@0: 
wolffd@0: % on small_fg, we have already included the evidence
wolffd@0: evidence = cell(1,T);
wolffd@0: tic; [engine{2}, ll(2)] = enter_evidence(engine{2}, evidence); toc
wolffd@0: 
wolffd@0: 
wolffd@0: % on small_bnet, we must add evidence to the dummy nodes 
wolffd@0: V = small_fg.nvars;
wolffd@0: dummy = V+1:V+small_fg.nfactors;
wolffd@0: N = max(dummy);
wolffd@0: evidence = cell(1, N);
wolffd@0: evidence(dummy) = {1};
wolffd@0: tic; [engine{3}, ll(3)] = enter_evidence(engine{3}, evidence); toc
wolffd@0: 
wolffd@0: 
wolffd@0: % on big_fg, use the original evidence
wolffd@0: evidence = cell(1, 2*T);
wolffd@0: evidence(onodes) = data(onodes);
wolffd@0: tic; [engine{4}, ll(4)] = enter_evidence(engine{4}, evidence); toc
wolffd@0: 
wolffd@0: 
wolffd@0: % on big_bnet, we must add evidence to the dummy nodes
wolffd@0: V = big_fg.nvars;
wolffd@0: assert(V == 2*T);
wolffd@0: dummy = V+1:V+big_fg.nfactors;
wolffd@0: N = max(dummy);
wolffd@0: evidence = cell(1, N);
wolffd@0: evidence(onodes) = data(onodes);
wolffd@0: evidence(dummy) = {1};
wolffd@0: tic; [engine{5}, ll(5)] = enter_evidence(engine{5}, evidence); toc
wolffd@0: 
wolffd@0: 
wolffd@0: marg = zeros(T, nengines, Q); % marg(t,e,:)
wolffd@0: for t=1:T
wolffd@0:   for e=1:nengines
wolffd@0:     m = marginal_nodes(engine{e}, t);
wolffd@0:     marg(t,e,:) = m.T;
wolffd@0:   end
wolffd@0: end
wolffd@0: marg(:,:,1)