% Construct various DBNs and examine their clique structure.% This was used to generate various figures in chap 3-4 of my thesis.% Examine the cliques in the unrolled mildew net%dbn = mk_mildew_dbn;dbn = mk_chmm(4);ss = dbn.nnodes_per_slice;T = 7;N = ss*T;bnet = dbn_to_bnet(dbn, T);constrained = 0;if constrained  stages = num2cell(unroll_set(1:ss, ss, T), 1);else  stages = { 1:N; };endclusters = {};%[jtree, root, cliques, B, w, elim_order, moral_edges, fill_in_edges] = ...%    dag_to_jtree(bnet, bnet.observed, stages, clusters);[jtree, root, cliques] =  graph_to_jtree(moralize(bnet.dag), ones(1,N), stages, clusters);flip=1;clf;[dummyx, dummyy, h] = draw_dbn(dbn.intra, dbn.inter, flip, T, -1);dir = '/home/eecs/murphyk/WP/Thesis/Figures/Inf/MildewUnrolled';mk_ps_from_clqs(dbn, T, cliques, [])%mk_collage_from_clqs(dir, cliques)% Examine the cliques in the cascade DBN% A-A%  \% B B%  \% C C%  \% D Dss = 4;intra = zeros(ss);inter = zeros(ss);inter(1, [1 2])=1;for i=2:ss-1  inter(i,i+1)=1;end% 2 coupled HMMs 1,3  and 2,4ss = 4;intra = zeros(ss);inter = zeros(ss); % no persistent edges%inter = diag(ones(ss,1)); % persitence edgesinter(1,3)=1; inter(3,1)=1;inter(2,4)=1; inter(4,2)=1;%bnet = mk_fhmm(3);bnet = mk_chmm(4);intra = bnet.intra;inter = bnet.inter;clqs = compute_minimal_interface(intra, inter);celldisp(clqs)% A A%  \% B B%  \% C C%  \% D-Dss = 4;intra = zeros(ss);inter = zeros(ss);for i=1:ss-1  inter(i,i+1)=1;endinter(4,4)=1;ns = 2*ones(1,ss);dbn = mk_dbn(intra, inter, ns);for i=2*ss  dbn.CPD{i} = tabular_CPD(bnet, i);endT = 4;N = ss*T;bnet = dbn_to_bnet(dbn, T);constrained = 1;if constrained  % elim first 3 slices first in any order  stages = {1:12, 13:16};  %stages = num2cell(unroll_set(1:ss, ss, T), 1);else  stages = { 1:N; };endclusters = {};%[jtree, root, cliques, B, w, elim_order, moral_edges, fill_in_edges] = ...%    dag_to_jtree(bnet, bnet.observed, stages, clusters);[jtree, root, cliques] =  graph_to_jtree(moralize(bnet.dag), ones(1,N), stages, clusters);% Examine the cliques in the 1.5 slice DBN%dbn = mk_mildew_dbn;dbn = mk_water_dbn;%dbn = mk_bat_dbn;ss = dbn.nnodes_per_slice;int = compute_fwd_interface(dbn);bnet15 = mk_slice_and_half_dbn(dbn, int);N = length(bnet15.dag);stages = {1:N};% bat%cl1 = [16 17 19 7 14];%cl2 = [27 25 21 23 20];%clusters = {cl1, cl2, cl1+ss, cl2+ss};% water%cl1 = 1:2; cl2 = 3:6; cl3 = 7:8;%clusters = {cl1, cl2, cl3, cl1+ss, cl2+ss, cl3+ss};%clusters = {};clusters = {int, int+ss};%[jtree, root, cliques, B, w, elim_order, moral_edges, fill_in_edges] = ...%    dag_to_jtree(bnet15, bnet.observed, stages, clusters);[jtree, root, cliques] =  graph_to_jtree(moralize(bnet15.dag), ones(1,N), stages, clusters);clq_len = [];for c=1:length(cliques)  clq_len(c) = length(cliques{c});endhist(clq_len, 1:max(clq_len));h=hist(clq_len, 1:max(clq_len));axis([1 max(clq_len)+1 0 max(h)+1])xlabel('clique size','fontsize',16)ylabel('number','fontsize',16)