% 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 mfatiny=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 mfaL0=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 codeassert(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