comparison toolboxes/FullBNT-1.0.7/bnt/examples/static/mfa1.m @ 0:e9a9cd732c1e tip

first hg version after svn

+% Factor analysis
+% Z -> X,  Z in R^k, X in R^D, k << D (high dimensional observations explained by small source)
+% Z ~ N(0,I),   X|Z ~ N(L z, Psi), where Psi is diagonal.
+%
+% Mixtures of FA
+% Now X|Z,W=i ~ N(mu(i) + L(i) Z, Psi(i))
+%
+% We compare to Zoubin Ghahramani's code.
+
+randn('state', 0);
+max_iter = 3;
+M = 2;
+k = 3;
+D = 5;
+
+n = 5;
+X1 = randn(n, D);
+X2 = randn(n, D) + 2; % move the mean to (2,2,2...)
+X = [X1; X2];
+N = size(X, 1);
+
+% initialise as in mfa
+tiny=exp(-700);
+mX = mean(X);
+cX=cov(X);
+scale=det(cX)^(1/D);
+randn('state',0); % must reset seed here so initial params are identical to mfa
+L0=randn(D*M,k)*sqrt(scale/k);
+W0 = permute(reshape(L0, [D M k]), [1 3 2]); % use D,K,M 
+Psi0=diag(cX)+tiny;
+Pi0=ones(M,1)/M;
+Mu0=randn(M,D)*sqrtm(cX)+ones(M,1)*mX;
+
+[Lh1, Ph1, Mu1, Pi1, LL1] = mfa(X,M,k,max_iter);
+Lh1 = permute(reshape(Lh1, [D M k]), [1 3 2]); % use D,K,M 
+
+
+ns = [M k D];
+dag = zeros(3);
+dag(1,3) = 1;
+dag(2,3) = 1;
+dnodes = 1;
+onodes = 3;
+
+bnet = mk_bnet(dag, ns, 'discrete', dnodes, 'observed', onodes);
+bnet.CPD{1} = tabular_CPD(bnet, 1, Pi0);
+
+%bnet.CPD{2} = gaussian_CPD(bnet, 2, zeros(k, 1), eye(k), [], 'diag', 'untied', 'clamp_mean',  'clamp_cov');
+
+bnet.CPD{2} = gaussian_CPD(bnet, 2, 'mean', zeros(k, 1), 'cov', eye(k), 'cov_type', 'diag', ...
+			   'cov_prior_weight', 0, 'clamp_mean', 1, 'clamp_cov', 1);
+
+%bnet.CPD{3} = gaussian_CPD(bnet, 3, Mu0', repmat(diag(Psi0), [1 1 M]), W0, 'diag', 'tied');
+
+bnet.CPD{3} = gaussian_CPD(bnet, 3, 'mean', Mu0', 'cov', repmat(diag(Psi0), [1 1 M]), ...
+			   'weights', W0, 'cov_type', 'diag', 'cov_prior_weight', 0, 'tied_cov', 1);
+
+engine = jtree_inf_engine(bnet);
+evidence = cell(3, N);
+evidence(3,:) = num2cell(X', 1);
+
+[bnet2, LL2, engine2] = learn_params_em(engine, evidence, max_iter);
+
+s = struct(bnet2.CPD{1});
+Pi2 = s.CPT(:);
+s = struct(bnet2.CPD{3});
+Mu2 = s.mean;
+W2 = s.weights;
+Sigma2 = s.cov;
+
+
+% Compare to Zoubin's code
+assert(approxeq(LL1,LL2));
+for i=1:M
+  assert(approxeq(W2(:,:,i), Lh1(:,:,i)));
+  assert(approxeq(Sigma2(:,:,i), diag(Ph1)));
+  assert(approxeq(Mu2(:,i), Mu1(i,:)));
+  assert(approxeq(Pi2(:), Pi1(:)));
+end
+