Daniel@0: % Fit a piece-wise linear regression model.
Daniel@0: % Here is the model
Daniel@0: %
Daniel@0: %  X \
Daniel@0: %  | |
Daniel@0: %  Q |
Daniel@0: %  | /
Daniel@0: %  Y
Daniel@0: %
Daniel@0: % where all arcs point down.
Daniel@0: % We condition everything on X, so X is a root node. Q is a softmax, and Y is a linear Gaussian.
Daniel@0: % Q is hidden, X and Y are observed.
Daniel@0: 
Daniel@0: X = 1;
Daniel@0: Q = 2;
Daniel@0: Y = 3;
Daniel@0: dag = zeros(3,3);
Daniel@0: dag(X,[Q Y]) = 1;
Daniel@0: dag(Q,Y) = 1;
Daniel@0: ns = [1 2 1]; % make X and Y scalars, and have 2 experts
Daniel@0: dnodes = [2];
Daniel@0: onodes = [1 3];
Daniel@0: bnet = mk_bnet(dag, ns, 'discrete', dnodes, 'observed', onodes);
Daniel@0: 
Daniel@0: IRLS_iter = 10;
Daniel@0: clamped = 0;
Daniel@0: 
Daniel@0: bnet.CPD{1} = root_CPD(bnet, 1);
Daniel@0: 
Daniel@0: % start with good initial params
Daniel@0: w = [-5 5];  % w(:,i) is the normal vector to the i'th decisions boundary
Daniel@0: b = [0 0];  % b(i) is the offset (bias) to the i'th decisions boundary
Daniel@0: 
Daniel@0: mu = [0 0];
Daniel@0: sigma = 1;
Daniel@0: Sigma = repmat(sigma*eye(ns(Y)), [ns(Y) ns(Y) ns(Q)]);
Daniel@0: W = [-1 1];
Daniel@0: W2 = reshape(W, [ns(Y) ns(X) ns(Q)]);
Daniel@0: 
Daniel@0: bnet.CPD{2} = softmax_CPD(bnet, 2, w, b,  clamped, IRLS_iter);
Daniel@0: bnet.CPD{3} = gaussian_CPD(bnet, 3, 'mean', mu, 'cov', Sigma, 'weights', W2);
Daniel@0: 
Daniel@0: 
Daniel@0: engine = jtree_inf_engine(bnet);
Daniel@0: 
Daniel@0: evidence = cell(1,3);
Daniel@0: evidence{X} = 0.68;
Daniel@0: 
Daniel@0: engine = enter_evidence(engine, evidence);
Daniel@0: 
Daniel@0: m = marginal_nodes(engine, Y);
Daniel@0: m.mu