comparison toolboxes/FullBNT-1.0.7/bnt/examples/static/StructLearn/model_select1.m @ 0:e9a9cd732c1e tip

first hg version after svn

+% Bayesian model selection demo.
+
+% We generate data from the model A->B
+% and compute the posterior prob of all 3 dags on 2 nodes:
+%  (1) A B,  (2) A <- B , (3) A -> B
+% Models 2 and 3 are Markov equivalent, and therefore indistinguishable from 
+% observational data alone.
+% Using the "difficult" params, the true model only gets a higher posterior after 2000 trials!
+% However, using the noisy NOT gate, the true model wins after 12 trials.
+
+% ground truth
+N = 2;
+dag = zeros(N);
+A = 1; B = 2; 
+dag(A,B) = 1;
+
+difficult = 0;
+if difficult
+  ntrials = 2000;
+  ns = 3*ones(1,N);
+  true_bnet = mk_bnet(dag, ns);
+  rand('state', 0);
+  temp = 5;
+  for i=1:N
+    %true_bnet.CPD{i} = tabular_CPD(true_bnet, i, temp);
+    true_bnet.CPD{i} = tabular_CPD(true_bnet, i);
+  end
+else
+  ntrials = 25;
+  ns = 2*ones(1,N);
+  true_bnet = mk_bnet(dag, ns);
+  true_bnet.CPD{1} = tabular_CPD(true_bnet, 1, [0.5 0.5]);
+  pfail = 0.1;
+  psucc = 1-pfail;
+  true_bnet.CPD{2} = tabular_CPD(true_bnet, 2, [pfail psucc; psucc pfail]); % NOT gate
+end
+
+G = mk_all_dags(N);
+nhyp = length(G);
+hyp_bnet = cell(1, nhyp);
+for h=1:nhyp
+  hyp_bnet{h} = mk_bnet(G{h}, ns);
+  for i=1:N
+    % We must set the CPTs to the mean of the prior for sequential log_marg_lik to be correct
+    % The BDeu prior is score equivalent, so models 2,3 will be indistinguishable.
+    % The uniform Dirichlet prior is not score equivalent...
+    fam = family(G{h}, i);
+    hyp_bnet{h}.CPD{i}= tabular_CPD(hyp_bnet{h}, i, 'prior_type', 'dirichlet', ...
+				    'CPT', 'unif');
+  end
+end
+prior = normalise(ones(1, nhyp));
+
+% save results before doing sequential updating
+init_hyp_bnet = hyp_bnet; 
+init_prior = prior;
+
+
+rand('state', 0);
+hyp_w = zeros(ntrials+1, nhyp);
+hyp_w(1,:) = prior(:)';
+
+data = zeros(N, ntrials);
+
+% First we compute the posteriors sequentially
+
+LL = zeros(1, nhyp);
+ll = zeros(1, nhyp);
+for t=1:ntrials
+  ev = cell2num(sample_bnet(true_bnet));
+  data(:,t) = ev;
+  for i=1:nhyp
+    ll(i) = log_marg_lik_complete(hyp_bnet{i}, ev);
+    hyp_bnet{i} = bayes_update_params(hyp_bnet{i}, ev);
+  end
+  prior = normalise(prior .* exp(ll));
+  LL = LL + ll;
+  hyp_w(t+1,:) = prior;
+end
+
+% Plot posterior model probabilities
+% Red = model 1 (no arcs), blue/green = models 2/3 (1 arc)
+% Blue = model 2 (2->1)
+% Green = model 3 (1->2, "ground truth")
+
+if 1
+  figure;
+m = size(hyp_w, 1);
+h=plot(1:m, hyp_w(:,1), 'r-',  1:m, hyp_w(:,2), 'b-.', 1:m, hyp_w(:,3), 'g:');
+axis([0 m   0 1])
+title('model posterior vs. time')
+%previewfig(gcf, 'format', 'png', 'height', 2, 'color', 'rgb')
+%exportfig(gcf, '/home/cs/murphyk/public_html/Bayes/Figures/model_select.png',...
+%'format', 'png', 'height', 2, 'color', 'rgb')
+drawnow
+end
+
+
+% Now check that batch updating gives same result
+hyp_bnet2 = init_hyp_bnet;
+prior2 = init_prior;
+
+cases = num2cell(data);
+LL2 = zeros(1, nhyp);
+for i=1:nhyp
+  LL2(i) = log_marg_lik_complete(hyp_bnet2{i}, cases);
+  hyp_bnet2{i} = bayes_update_params(hyp_bnet2{i}, cases);
+end
+
+
+assert(approxeq(LL, LL2))
+LL
+
+for i=1:nhyp
+  for j=1:N
+    s1 = struct(hyp_bnet{i}.CPD{j});
+    s2 = struct(hyp_bnet2{i}.CPD{j});
+    assert(approxeq(s1.CPT, s2.CPT))
+  end
+end
+