comparison toolboxes/FullBNT-1.0.7/netlabKPM/evidence_weighted.m @ 0:e9a9cd732c1e tip

first hg version after svn

+function [net, gamma, logev] = evidence_weighted(net, x, t, eso_w, num)
+%EVIDENCE Re-estimate hyperparameters using evidence approximation.
+%
+%	Description
+%	[NET] = EVIDENCE(NET, X, T) re-estimates the hyperparameters ALPHA
+%	and BETA by applying Bayesian re-estimation formulae for NUM
+%	iterations. The hyperparameter ALPHA can be a simple scalar
+%	associated with an isotropic prior on the weights, or can be a vector
+%	in which each component is associated with a group of weights as
+%	defined by the INDEX matrix in the NET data structure. These more
+%	complex priors can be set up for an MLP using MLPPRIOR. Initial
+%	values for the iterative re-estimation are taken from the network
+%	data structure NET passed as an input argument, while the return
+%	argument NET contains the re-estimated values.
+%
+%	[NET, GAMMA, LOGEV] = EVIDENCE(NET, X, T, NUM) allows the re-
+%	estimation  formula to be applied for NUM cycles in which the re-
+%	estimated values for the hyperparameters from each cycle are used to
+%	re-evaluate the Hessian matrix for the next cycle.  The return value
+%	GAMMA is the number of well-determined parameters and LOGEV is the
+%	log of the evidence.
+%
+%	See also
+%	MLPPRIOR, NETGRAD, NETHESS, DEMEV1, DEMARD
+%
+
+%	Copyright (c) Ian T Nabney (1996-9)
+
+errstring = consist(net, '', x, t);
+if ~isempty(errstring)
+  error(errstring);
+end
+
+ndata = size(x, 1);
+if nargin == 4
+  num = 1;
+end
+
+if isfield(net,'beta')
+    beta = net.beta;
+else 
+    beta = 1;
+end;
+
+% Extract weights from network
+pakstr = [net.type, 'pak'];
+w = feval(pakstr, net);
+
+% Evaluate data-dependent contribution to the Hessian matrix.
+[h, dh] = nethess_weighted(w, net, x, t, eso_w); 
+
+% Now set the negative eigenvalues to zero.
+[evec, evl] = eig(dh);
+evl = evl.*(evl > 0);
+% safe_evl is used to avoid taking log of zero
+safe_evl = evl + eps.*(evl <= 0);
+
+% Do the re-estimation. 
+for k = 1 : num
+  [e, edata, eprior] = neterr_weighted(w, net, x, t, eso_w);
+  h = nethess_weighted(w, net, x, t, eso_w, dh);
+  % Re-estimate alpha.
+  if size(net.alpha) == [1 1]
+    % Evaluate number of well-determined parameters.
+    if k == 1
+      % Form vector of eigenvalues
+      evl = diag(evl);
+      safe_evl = diag(safe_evl);
+    end
+    B = beta*evl;
+    gamma = sum(B./(B + net.alpha));       
+    net.alpha = 0.5*gamma/eprior;
+       
+    % Partially evaluate log evidence
+    logev = e - 0.5*sum(log(safe_evl)) + 0.5*net.nwts*log(net.alpha) - ...
+      0.5*ndata*log(2*pi);
+  else
+    ngroups = size(net.alpha, 1);
+    gams = zeros(1, ngroups);
+    logas = zeros(1, ngroups);
+    traces = zeros(1, ngroups);
+    % Reconstruct data hessian with negative eigenvalues set to zero.
+    dh = evec*evl*evec';
+    hinv = inv(nethess_weighted(w, net, x, t, eso_w, dh));
+    for m = 1 : ngroups
+      group_nweights = sum(net.index(:, m));
+      gams(m) = group_nweights - ...
+	        net.alpha(m)*sum(diag(hinv).*net.index(:,m));
+      net.alpha(m) = real(gams(m)/(2*eprior(m)));
+      % Weight alphas by number of weights in group
+      logas(m) = 0.5*group_nweights*log(net.alpha(m));
+      % Compute sum of evalues corresponding to group
+      traces(m) = sum(log(safe_evl*net.index(:,m)));
+    end 
+    gamma = sum(gams, 2);
+    logev = e - 0.5*sum(traces) + sum(logas) - 0.5*ndata*log(2*pi);
+  end
+  % Re-estimate beta.
+  if isfield(net, 'beta')
+      net.beta = 0.5*(net.nout*ndata - gamma)/edata;
+  end
+  logev = logev + 0.5*ndata*log(beta);
+end
+