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1 % make a factor graph corresponding to an HMM with Gaussian outputs, where we absorb the
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2 % evidence up front
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3
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4 seed = 1;
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5 rand('state', seed);
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6 randn('state', seed);
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7
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8 T = 3;
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9 Q = 3;
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10 O = 2;
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11 cts_obs = 1;
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12 param_tying = 1;
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13 bnet = mk_hmm_bnet(T, Q, O, cts_obs, param_tying);
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14 N = 2*T;
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15 onodes = bnet.observed;
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16 hnodes = mysetdiff(1:N, onodes);
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17
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18 data = sample_bnet(bnet);
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19
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20 init_factor = bnet.CPD{1};
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21 obs_factor = bnet.CPD{3};
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22 edge_factor = bnet.CPD{2}; % trans matrix
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23
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24 nfactors = T;
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25 nvars = T; % hidden only
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26 G = zeros(nvars, nfactors);
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27 G(1,1) = 1;
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28 for t=1:T-1
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29 G(t:t+1, t+1)=1;
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30 end
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31
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32 node_sizes = Q*ones(1,T);
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33
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34 % We tie params as follows:
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35 % the first hidden node use init_factor (number 1)
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36 % all hidden nodes on the backbone use edge_factor (number 2)
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37 % all observed nodes use the same factor, namely obs_factor
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38
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39 small_fg = mk_fgraph_given_ev(G, node_sizes, {init_factor, edge_factor}, {obs_factor}, data(onodes), ...
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40 'equiv_class', [1 2*ones(1,T-1)], 'ev_equiv_class', ones(1,T));
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41
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42 small_bnet = fgraph_to_bnet(small_fg);
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43
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44 % don't pre-process evidence
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45 % big_fg = bnet_to_fgraph(bnet); % can't handle Gaussian node
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46
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47
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48 engine = {};
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49 engine{1} = jtree_inf_engine(bnet);
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50 engine{2} = belprop_fg_inf_engine(small_fg, 'max_iter', 2*T);
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51 engine{3} = jtree_inf_engine(small_bnet);
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52 nengines = length(engine);
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53
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54
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55 % on BN, use the original evidence
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56 evidence = cell(1, 2*T);
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57 evidence(onodes) = data(onodes);
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58 tic; [engine{1}, ll(1)] = enter_evidence(engine{1}, evidence); toc
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59
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60
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61 % on small_fg, we have already included the evidence
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62 evidence = cell(1,T);
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63 tic; [engine{2}, ll(2)] = enter_evidence(engine{2}, evidence); toc
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64
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65
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66 % on small_bnet, we must add evidence to the dummy nodes
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67 V = small_fg.nvars;
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68 dummy = V+1:V+small_fg.nfactors;
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69 N = max(dummy);
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70 evidence = cell(1, N);
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71 evidence(dummy) = {1};
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72 tic; [engine{3}, ll(3)] = enter_evidence(engine{3}, evidence); toc
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73
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74
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75
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76 marg = zeros(T, nengines, Q); % marg(t,e,:)
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77 for t=1:T
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78 for e=1:nengines
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79 m = marginal_nodes(engine{e}, t);
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80 marg(t,e,:) = m.T;
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81 end
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82 end
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83 marg(:,:,1)
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