comparison toolboxes/FullBNT-1.0.7/bnt/examples/static/mixexp1.m @ 0:e9a9cd732c1e tip

first hg version after svn

+% Fit a piece-wise linear regression model.
+% Here is the model
+%
+%  X \
+%  | |
+%  Q |
+%  | /
+%  Y
+%
+% where all arcs point down.
+% We condition everything on X, so X is a root node. Q is a softmax, and Y is a linear Gaussian.
+% Q is hidden, X and Y are observed.
+
+X = 1;
+Q = 2;
+Y = 3;
+dag = zeros(3,3);
+dag(X,[Q Y]) = 1;
+dag(Q,Y) = 1;
+ns = [1 2 1]; % make X and Y scalars, and have 2 experts
+dnodes = [2];
+onodes = [1 3];
+bnet = mk_bnet(dag, ns, 'discrete', dnodes, 'observed', onodes);
+
+
+w = [-5 5];  % w(:,i) is the normal vector to the i'th decisions boundary
+b = [0 0];  % b(i) is the offset (bias) to the i'th decisions boundary
+
+mu = [0 0];
+sigma = 1;
+Sigma = repmat(sigma*eye(ns(Y)), [ns(Y) ns(Y) ns(Q)]);
+W = [-1 1];
+W2 = reshape(W, [ns(Y) ns(X) ns(Q)]);
+
+bnet.CPD{1} = root_CPD(bnet, 1);
+bnet.CPD{2} = softmax_CPD(bnet, 2, w, b);
+bnet.CPD{3} = gaussian_CPD(bnet, 3, 'mean', mu, 'cov', Sigma, 'weights', W2);
+
+
+
+% Check inference
+
+x = 0.1;
+ystar = 1;
+
+engine = jtree_inf_engine(bnet);
+[engine, loglik] = enter_evidence(engine, {x, [], ystar});
+Qpost = marginal_nodes(engine, 2);
+
+% eta(i,:) = softmax (gating) params for expert i
+eta = [b' w'];
+
+% theta(i,:) = regression vector for expert i
+theta = [mu' W'];
+
+% yhat(i) = E[y | Q=i, x] = prediction of i'th expert
+x1 = [1 x]';
+yhat = theta * x1;
+
+% gate_prior(i,:) = Pr(Q=i | x)
+gate_prior = normalise(exp(eta * x1));
+
+% cond_lik(i) = Pr(y | Q=i, x)
+cond_lik = (1/(sqrt(2*pi)*sigma)) * exp(-(0.5/sigma^2) * ((ystar - yhat) .* (ystar - yhat)));
+
+% gate_posterior(i,:) = Pr(Q=i | x, y)
+[gate_posterior, lik] = normalise(gate_prior .* cond_lik);
+
+assert(approxeq(gate_posterior(:), Qpost.T(:)));
+assert(approxeq(log(lik), loglik));
+
+