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1 % Factor analysis
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2 % Z -> X, Z in R^k, X in R^D, k << D (high dimensional observations explained by small source)
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3 % Z ~ N(0,I), X|Z ~ N(L z, Psi), where Psi is diagonal.
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4 %
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5 % Mixtures of FA
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6 % Now X|Z,W=i ~ N(mu(i) + L(i) Z, Psi(i))
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7 %
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8 % We compare to Zoubin Ghahramani's code.
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9
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10 randn('state', 0);
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11 max_iter = 3;
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12 M = 2;
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13 k = 3;
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14 D = 5;
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15
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16 n = 5;
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17 X1 = randn(n, D);
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18 X2 = randn(n, D) + 2; % move the mean to (2,2,2...)
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19 X = [X1; X2];
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20 N = size(X, 1);
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21
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22 % initialise as in mfa
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23 tiny=exp(-700);
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24 mX = mean(X);
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25 cX=cov(X);
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26 scale=det(cX)^(1/D);
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27 randn('state',0); % must reset seed here so initial params are identical to mfa
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28 L0=randn(D*M,k)*sqrt(scale/k);
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29 W0 = permute(reshape(L0, [D M k]), [1 3 2]); % use D,K,M
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30 Psi0=diag(cX)+tiny;
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31 Pi0=ones(M,1)/M;
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32 Mu0=randn(M,D)*sqrtm(cX)+ones(M,1)*mX;
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33
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34 [Lh1, Ph1, Mu1, Pi1, LL1] = mfa(X,M,k,max_iter);
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35 Lh1 = permute(reshape(Lh1, [D M k]), [1 3 2]); % use D,K,M
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36
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37
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38 ns = [M k D];
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39 dag = zeros(3);
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40 dag(1,3) = 1;
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41 dag(2,3) = 1;
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42 dnodes = 1;
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43 onodes = 3;
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44
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45 bnet = mk_bnet(dag, ns, 'discrete', dnodes, 'observed', onodes);
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46 bnet.CPD{1} = tabular_CPD(bnet, 1, Pi0);
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47
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48 %bnet.CPD{2} = gaussian_CPD(bnet, 2, zeros(k, 1), eye(k), [], 'diag', 'untied', 'clamp_mean', 'clamp_cov');
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49
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50 bnet.CPD{2} = gaussian_CPD(bnet, 2, 'mean', zeros(k, 1), 'cov', eye(k), 'cov_type', 'diag', ...
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51 'cov_prior_weight', 0, 'clamp_mean', 1, 'clamp_cov', 1);
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52
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53 %bnet.CPD{3} = gaussian_CPD(bnet, 3, Mu0', repmat(diag(Psi0), [1 1 M]), W0, 'diag', 'tied');
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54
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55 bnet.CPD{3} = gaussian_CPD(bnet, 3, 'mean', Mu0', 'cov', repmat(diag(Psi0), [1 1 M]), ...
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56 'weights', W0, 'cov_type', 'diag', 'cov_prior_weight', 0, 'tied_cov', 1);
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57
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58 engine = jtree_inf_engine(bnet);
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59 evidence = cell(3, N);
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60 evidence(3,:) = num2cell(X', 1);
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61
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62 [bnet2, LL2, engine2] = learn_params_em(engine, evidence, max_iter);
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63
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64 s = struct(bnet2.CPD{1});
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65 Pi2 = s.CPT(:);
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66 s = struct(bnet2.CPD{3});
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67 Mu2 = s.mean;
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68 W2 = s.weights;
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69 Sigma2 = s.cov;
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70
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71
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72 % Compare to Zoubin's code
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73 assert(approxeq(LL1,LL2));
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74 for i=1:M
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75 assert(approxeq(W2(:,:,i), Lh1(:,:,i)));
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76 assert(approxeq(Sigma2(:,:,i), diag(Ph1)));
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77 assert(approxeq(Mu2(:,i), Mu1(i,:)));
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78 assert(approxeq(Pi2(:), Pi1(:)));
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79 end
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80
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