comparison toolboxes/FullBNT-1.0.7/bnt/examples/dynamic/HHMM/hhmm_jtree_clqs.m @ 0:e9a9cd732c1e tip

first hg version after svn

+% Find out how big the cliques are in an HHMM as a function of depth
+% (This is how we get the complexity bound of O(D K^{1.5D}).)
+
+if 0
+Qsize = [];
+Fsize = [];
+Nclqs = [];
+end
+
+ds = 1:15;
+
+for d = ds
+  allQ = 1;
+  [intra, inter, Qnodes, Fnodes, Onode] = mk_hhmm_topo(d, allQ);
+  
+  N = length(intra);
+  ns = 2*ones(1,N);
+  
+  bnet = mk_dbn(intra, inter, ns);
+  for i=1:N
+    bnet.CPD{i} = tabular_CPD(bnet, i);
+  end
+  
+  if 0
+    T = 5;
+    dag = unroll_dbn_topology(intra, inter, T);
+    engine = jtree_unrolled_dbn_inf_engine(bnet, T, 'constrained', 1);
+    S = struct(engine);
+    S1 = struct(S.sub_engine);
+  end
+  
+  engine = jtree_dbn_inf_engine(bnet);
+  S = struct(engine);
+  J = S.jtree_struct;
+  
+  ss = 2*d+1;
+  Qnodes2 = Qnodes + ss;
+  QQnodes = [Qnodes Qnodes2];
+  
+  % find out how many Q nodes in each clique, and how many F nodes
+  C = length(J.cliques);
+  Nclqs(d) = 0;
+  for c=1:C
+    Qsize(c,d) = length(myintersect(J.cliques{c}, QQnodes));
+    Fsize(c,d) = length(myintersect(J.cliques{c}, Fnodes));
+    if length(J.cliques{c}) > 1 % exclude observed leaves
+      Nclqs(d) = Nclqs(d) + 1;
+    end
+  end
+  %pred_max_Qsize(d) = ceil(d+(d+1)/2);
+  pred_max_Qsize(d) = ceil(1.5*d);
+  
+  fprintf('d=%d\n', d);
+  %fprintf('D=%d, max F = %d. max Q = %d, pred max Q = %d\n', ...
+	%  D, max(Fsize), max(Qsize), ceil(D+(D+1)/2));
+	     
+  %histc(Qsize,1:max(Qsize)) % how many of each size?
+end % next d
+
+
+Q = 2;
+pred_mass = ds.*(Q.^ds) + Q.^(ceil(1.5 * ds))
+pred_mass2 = Q.^(ceil(1.5 * ds))
+
+for d=ds
+  mass(d) = 0;
+  for c=1:C
+    mass(d) = mass(d) + Q^Qsize(c,d);
+  end
+end
+    
+
+if 0
+%plot(ds, max(Qsize), 'o-',  ds, pred_max_Qsize, '*--');
+%plot(ds, max(Qsize), 'o-',  ds, 1.5*ds, '*--');
+%plot(ds, mass, 'o-',  ds, pred_mass, '*--');
+D = 15;
+%plot(ds(1:D), mass(1:D), 'bo-',  ds(1:D), pred_mass(1:D), 'g*--', ds(1:D), pred_mass2(1:D), 'k+-.');
+plot(ds(1:D), log(mass(1:D)), 'bo-',  ds(1:D), log(pred_mass(1:D)), 'g*--', ds(1:D), log(pred_mass2(1:D)), 'k+-.');
+
+grid on
+xlabel('depth of hierarchy')
+title('max num Q nodes in any clique vs. depth')
+legend('actual', 'predicted')
+
+%previewfig(gcf, 'width', 3, 'height', 1.5, 'color', 'bw');
+%exportfig(gcf, '/home/cs/murphyk/WP/ConferencePapers/HHMM/clqsize2.eps', ...
+%          'width', 3, 'height', 1.5, 'color', 'bw');   
+
+end
+
+
+if 0
+for d=ds
+  effnumclqs(d) = length(find(Qsize(:,d)>0));
+end
+ds = 1:10;
+Qs = 2:10;
+maxC = size(Qsize, 1);
+cost = [];
+cost_bound = [];
+for qi=1:length(Qs)
+  Q = Qs(qi);
+  for d=ds
+    cost(d,qi) = 0;
+    for c=1:maxC
+      if length(Qsize(c,d) > 0) % this clique contains Q nodes
+	cost(d,qi) = cost(d,qi) + Q^Qsize(c,d)*2^Fsize(c,d);
+      end
+    end
+    %cost_bound(d,qi) = effnumclqs(d) * 8 * Q^(max(Qsize(:,d)));
+    cost_bound(d,qi) = (effnumclqs(d)*8) + Q^(max(Qsize(:,d)));
+  end
+end
+
+qi=2; plot(ds, cost(:,qi), 'o-',  ds, cost_bound(:,qi), '*--');
+end
+
+
+if 0
+% convert numbers in cliques into names
+for d=1:D
+  Fdecode(Fnodes(d)) = d;
+end
+for c=8:15
+  clqs = J.cliques{c};
+  fprintf('clique %d: ', c);
+  for k=clqs
+    if myismember(k, Qnodes)
+      fprintf('Q%d ', k)
+    elseif myismember(k, Fnodes)
+      fprintf('F%d ', Fdecode(k))
+    elseif isequal(k, Onode)
+      fprintf('O ')
+    elseif myismember(k, Qnodes2)
+      fprintf('Q%d* ', k-ss)
+    else
+      error(['unrecognized node ' k])
+    end
+  end
+  fprintf('\n');
+end
+end