diff toolboxes/FullBNT-1.0.7/bnt/examples/static/Misc/mixexp_graddesc.m @ 0:e9a9cd732c1e tip

first hg version after svn

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolboxes/FullBNT-1.0.7/bnt/examples/static/Misc/mixexp_graddesc.m	Tue Feb 10 15:05:51 2015 +0000
@@ -0,0 +1,51 @@
+
+%%%%%%%%%%
+
+function [theta, eta] = mixture_of_experts(q, data, num_iter, theta, eta)
+% MIXTURE_OF_EXPERTS Fit a piecewise linear regression model using stochastic gradient descent.
+% [theta, eta] = mixture_of_experts(q, data, num_iter)
+%
+% Inputs:
+% q = number of pieces (experts)
+% data(l,:) = input example l 
+% 
+% Outputs:
+% theta(i,:) = regression vector for expert i
+% eta(i,:) = softmax (gating) params for expert i
+
+[num_cases dim] = size(data);
+data = [ones(num_cases,1) data]; % prepend with offset
+mu = 0.5; % step size
+sigma = 1; % variance of noise
+
+if nargin < 4
+  theta = 0.1*rand(q, dim);
+  eta = 0.1*rand(q, dim);
+end
+
+for t=1:num_iter
+  for iter=1:num_cases
+    x = data(iter, 1:dim);
+    ystar = data(iter, dim+1); % target
+    % yhat(i) = E[y | Q=i, x] = prediction of i'th expert
+    yhat = theta * x'; 
+    % gate_prior(i,:) = Pr(Q=i | x)
+    gate_prior = exp(eta * x');
+    gate_prior = gate_prior / sum(gate_prior);
+    % lik(i) = Pr(y | Q=i, x)
+    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 = gate_prior .* lik;
+    gate_posterior = gate_posterior / sum(gate_posterior);
+    % Update
+    eta = eta + mu*(gate_posterior - gate_prior)*x;
+    theta = theta + mu*(gate_posterior .* (ystar - yhat))*x;
+  end
+
+  if mod(t,100)==0
+    fprintf(1, 'iter %d\n', t);
+  end
+
+end
+fprintf(1, '\n');
+