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1 % Make a DBN with the following inter-connectivity matrix
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2 % 1
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3 % / \
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4 % 2 3
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5 % \ /
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6 % 4
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7 % |
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8 % 5
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9 % where all arcs point down. In addition, there are persistence arcs from each node to itself.
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10 % There are no intra-slice connections.
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11 % Nodes have noisy-or CPDs.
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12 % Node 1 turns on spontaneously due to its leaky source.
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13 % This effect trickles down to the other nodes in the order shown.
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14 % All the other nodes inhibit their leaks.
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15 % None of the nodes inhibit the connection from themselves, so that once they are on, they remain
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16 % on (persistence).
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17 %
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18 % This model was used in the experiments reported in
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19 % - "Learning the structure of DBNs", Friedman, Murphy and Russell, UAI 1998.
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20 % where the structure was learned even in the presence of missing data.
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21 % In that paper, we used the structural EM algorithm.
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22 % Here, we assume full observability and tabular CPDs for the learner, so we can use a much
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23 % simpler learning algorithm.
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24
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25 ss = 5;
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26
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27 inter = eye(ss);
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28 inter(1,[2 3]) = 1;
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29 inter(2,4)=1;
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30 inter(3,4)=1;
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31 inter(4,5)=1;
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32
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33 intra = zeros(ss);
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34 ns = 2*ones(1,ss);
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35
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36 bnet = mk_dbn(intra, inter, ns);
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37
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38 % All nodes start out off
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39 for i=1:ss
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40 bnet.CPD{i} = tabular_CPD(bnet, i, [1.0 0.0]');
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41 end
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42
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43 % The following params correspond to Fig 4a in the UAI 98 paper
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44 % The first arg is the leak inhibition prob.
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45 % The vector contains the inhib probs from the parents in the previous slice;
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46 % the last element is self, which is never inhibited.
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47 bnet.CPD{1+ss} = noisyor_CPD(bnet, 1+ss, 0.8, 0);
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48 bnet.CPD{2+ss} = noisyor_CPD(bnet, 2+ss, 1, [0.9 0]);
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49 bnet.CPD{3+ss} = noisyor_CPD(bnet, 3+ss, 1, [0.8 0]);
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50 bnet.CPD{4+ss} = noisyor_CPD(bnet, 4+ss, 1, [0.7 0.6 0]);
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51 bnet.CPD{5+ss} = noisyor_CPD(bnet, 5+ss, 1, [0.5 0]);
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52
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53
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54 % Generate some training data
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55
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56 nseqs = 20;
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57 seqs = cell(1,nseqs);
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58 T = 30;
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59 for i=1:nseqs
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60 seqs{i} = sample_dbn(bnet, T);
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61 end
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62
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63 max_fan_in = 3; % let's cheat a little here
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64
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65 % computing num. incorrect edges as a fn of the size of the training set
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66 %sz = [5 10 15 20];
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67 sz = [5 10];
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68 h = zeros(1, length(sz));
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69 for i=1:length(sz)
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70 inter2 = learn_struct_dbn_reveal(seqs(1:sz(i)), ns, max_fan_in);
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71 h(i) = sum(abs(inter(:)-inter2(:))); % hamming distance
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72 end
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73 h
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