comparison toolboxes/FullBNT-1.0.7/bnt/examples/static/fa1.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.
+%
+% We compare to Zoubin Ghahramani's code.
+
+state = 0;
+rand('seed', state);
+randn('seed', state);
+max_iter = 3;
+k = 2;
+D = 4;
+N = 10;
+X = randn(N, D);
+
+% Initialize as in Zoubin's ffa (fast factor analysis)
+X=X-ones(N,1)*mean(X);
+XX=X'*X/N;
+diagXX=diag(XX);
+cX=cov(X);
+scale=det(cX)^(1/D);
+randn('seed', 0);  % must reset seed here so initial params are identical to mfa
+L0=randn(D,k)*sqrt(scale/k);
+W0 = L0;
+Psi0=diag(cX);
+
+[L1, Psi1, LL1] = ffa(X,k,max_iter);
+
+
+ns = [k D];
+dag = zeros(2,2);
+dag(1,2) = 1;
+bnet = mk_bnet(dag, ns, 'discrete', [], 'observed', 2);
+bnet.CPD{1} = gaussian_CPD(bnet, 1, 'mean', zeros(k,1), 'cov', eye(k), 'cov_type', 'diag', ...
+			   'clamp_mean', 1, 'clamp_cov', 1);
+bnet.CPD{2} = gaussian_CPD(bnet, 2, 'mean', zeros(D,1), 'cov', diag(Psi0), 'weights', W0, ...
+			   'cov_type', 'diag', 'cov_prior_weight', 0, 'clamp_mean', 1);
+
+engine = jtree_inf_engine(bnet);
+evidence = cell(2,N);
+evidence(2,:) = num2cell(X', 1);
+
+[bnet2, LL2] = learn_params_em(engine, evidence, max_iter);
+
+s = struct(bnet2.CPD{2});
+L2 = s.weights;
+Psi2 = s.cov;
+
+
+
+% Compare to Zoubin's code
+assert(approxeq(LL2, LL1));
+assert(approxeq(Psi2, diag(Psi1)));
+assert(approxeq(L2, L1));
+
+
+