Daniel@0: % Make a DBN with the following inter-connectivity matrix
Daniel@0: %    1
Daniel@0: %   /  \
Daniel@0: %  2   3
Daniel@0: %   \ /
Daniel@0: %    4 
Daniel@0: %    |
Daniel@0: %    5
Daniel@0: % where all arcs point down. In addition, there are persistence arcs from each node to itself.
Daniel@0: % There are no intra-slice connections.
Daniel@0: % Nodes have noisy-or CPDs.
Daniel@0: % Node 1 turns on spontaneously due to its leaky source.
Daniel@0: % This effect trickles down to the other nodes in the order shown.
Daniel@0: % All the other nodes inhibit their leaks.
Daniel@0: % None of the nodes inhibit the connection from themselves, so that once they are on, they remain
Daniel@0: % on (persistence).
Daniel@0: %
Daniel@0: % This model was used in the experiments reported in
Daniel@0: % - "Learning the structure of DBNs", Friedman, Murphy and Russell, UAI 1998.
Daniel@0: % where the structure was learned even in the presence of missing data.
Daniel@0: % In that paper, we used the structural EM algorithm.
Daniel@0: % Here, we assume full observability and tabular CPDs for the learner, so we can use a much
Daniel@0: % simpler learning algorithm.
Daniel@0: 
Daniel@0: ss = 5;
Daniel@0: 
Daniel@0: inter = eye(ss);
Daniel@0: inter(1,[2 3]) = 1;
Daniel@0: inter(2,4)=1;
Daniel@0: inter(3,4)=1;
Daniel@0: inter(4,5)=1;
Daniel@0: 
Daniel@0: intra = zeros(ss);
Daniel@0: ns = 2*ones(1,ss);
Daniel@0: 
Daniel@0: bnet = mk_dbn(intra, inter, ns);
Daniel@0: 
Daniel@0: % All nodes start out off
Daniel@0: for i=1:ss
Daniel@0:   bnet.CPD{i} = tabular_CPD(bnet, i, [1.0 0.0]');
Daniel@0: end
Daniel@0: 
Daniel@0: % The following params correspond to Fig 4a in the UAI 98 paper
Daniel@0: % The first arg is the leak inhibition prob.
Daniel@0: % The vector contains the inhib probs from the parents in the previous slice;
Daniel@0: % the last element is self, which is never inhibited.
Daniel@0: bnet.CPD{1+ss} = noisyor_CPD(bnet, 1+ss, 0.8, 0);
Daniel@0: bnet.CPD{2+ss} = noisyor_CPD(bnet, 2+ss, 1, [0.9 0]);
Daniel@0: bnet.CPD{3+ss} = noisyor_CPD(bnet, 3+ss, 1, [0.8 0]);
Daniel@0: bnet.CPD{4+ss} = noisyor_CPD(bnet, 4+ss, 1, [0.7 0.6 0]);
Daniel@0: bnet.CPD{5+ss} = noisyor_CPD(bnet, 5+ss, 1, [0.5 0]);
Daniel@0: 
Daniel@0: 
Daniel@0: % Generate some training data
Daniel@0: 
Daniel@0: nseqs = 20;
Daniel@0: seqs = cell(1,nseqs);
Daniel@0: T = 30;
Daniel@0: for i=1:nseqs
Daniel@0:   seqs{i} = sample_dbn(bnet, T);
Daniel@0: end
Daniel@0: 
Daniel@0: max_fan_in = 3; % let's cheat a little here
Daniel@0: 
Daniel@0: % computing num. incorrect edges as a fn of the size of the training set
Daniel@0: %sz = [5 10 15 20];    
Daniel@0: sz = [5 10];    
Daniel@0: h = zeros(1, length(sz));
Daniel@0: for i=1:length(sz)
Daniel@0:   inter2 = learn_struct_dbn_reveal(seqs(1:sz(i)), ns, max_fan_in);
Daniel@0:   h(i) = sum(abs(inter(:)-inter2(:))); % hamming distance
Daniel@0: end
Daniel@0: h