comparison toolboxes/FullBNT-1.0.7/netlab3.3/glmhess.m @ 0:e9a9cd732c1e tip

first hg version after svn

+function [h, hdata] = glmhess(net, x, t, hdata)
+%GLMHESS Evaluate the Hessian matrix for a generalised linear model.
+%
+%	Description
+%	H = GLMHESS(NET, X, T) takes a GLM network data structure NET,   a
+%	matrix X of input values, and a matrix T of target values and returns
+%	the full Hessian matrix H corresponding to the second derivatives of
+%	the negative log posterior distribution, evaluated for the current
+%	weight and bias values as defined by NET. Note that the target data
+%	is not required in the calculation, but is included to make the
+%	interface uniform with NETHESS.  For linear and logistic outputs, the
+%	computation is very simple and is  done (in effect) in one line in
+%	GLMTRAIN.
+%
+%	[H, HDATA] = GLMHESS(NET, X, T) returns both the Hessian matrix H and
+%	the contribution HDATA arising from the data dependent term in the
+%	Hessian.
+%
+%	H = GLMHESS(NET, X, T, HDATA) takes a network data structure NET, a
+%	matrix X of input values, and a matrix T of  target values, together
+%	with the contribution HDATA arising from the data dependent term in
+%	the Hessian, and returns the full Hessian matrix H corresponding to
+%	the second derivatives of the negative log posterior distribution.
+%	This version saves computation time if HDATA has already been
+%	evaluated for the current weight and bias values.
+%
+%	See also
+%	GLM, GLMTRAIN, HESSCHEK, NETHESS
+%
+
+%	Copyright (c) Ian T Nabney (1996-2001)
+
+% Check arguments for consistency
+errstring = consist(net, 'glm', x, t);
+if ~isempty(errstring);
+  error(errstring);
+end
+
+ndata = size(x, 1);
+nparams = net.nwts;
+nout = net.nout;
+p = glmfwd(net, x);
+inputs = [x ones(ndata, 1)];
+
+if nargin == 3
+   hdata = zeros(nparams);	% Full Hessian matrix
+   % Calculate data component of Hessian
+   switch net.outfn
+
+   case 'linear'
+      % No weighting function here
+      out_hess = [x ones(ndata, 1)]'*[x ones(ndata, 1)];
+      for j = 1:nout
+         hdata = rearrange_hess(net, j, out_hess, hdata);
+      end
+   case 'logistic'
+      % Each output is independent
+      e = ones(1, net.nin+1);
+      link_deriv = p.*(1-p);
+      out_hess = zeros(net.nin+1);
+      for j = 1:nout
+         inputs = [x ones(ndata, 1)].*(sqrt(link_deriv(:,j))*e);
+         out_hess = inputs'*inputs;   % Hessian for this output
+         hdata = rearrange_hess(net, j, out_hess, hdata);
+      end
+      
+   case 'softmax'
+      bb_start = nparams - nout + 1;	% Start of bias weights block
+      ex_hess = zeros(nparams);	% Contribution to Hessian from single example
+      for m = 1:ndata
+         X = x(m,:)'*x(m,:);
+         a = diag(p(m,:))-((p(m,:)')*p(m,:));
+         ex_hess(1:nparams-nout,1:nparams-nout) = kron(a, X);
+         ex_hess(bb_start:nparams, bb_start:nparams) = a.*ones(net.nout, net.nout);
+         temp = kron(a, x(m,:));
+         ex_hess(bb_start:nparams, 1:nparams-nout) = temp;
+         ex_hess(1:nparams-nout, bb_start:nparams) = temp';
+         hdata = hdata + ex_hess;
+      end
+    otherwise
+      error(['Unknown activation function ', net.outfn]);
+    end
+end
+
+[h, hdata] = hbayes(net, hdata);
+
+function hdata = rearrange_hess(net, j, out_hess, hdata)
+
+% Because all the biases come after all the input weights,
+% we have to rearrange the blocks that make up the network Hessian.
+% This function assumes that we are on the jth output and that all outputs
+% are independent.
+
+bb_start = net.nwts - net.nout + 1;	% Start of bias weights block
+ob_start = 1+(j-1)*net.nin; 	% Start of weight block for jth output
+ob_end = j*net.nin;         	% End of weight block for jth output
+b_index = bb_start+(j-1);   	% Index of bias weight
+% Put input weight block in right place
+hdata(ob_start:ob_end, ob_start:ob_end) = out_hess(1:net.nin, 1:net.nin);
+% Put second derivative of bias weight in right place
+hdata(b_index, b_index) = out_hess(net.nin+1, net.nin+1);
+% Put cross terms (input weight v bias weight) in right place
+hdata(b_index, ob_start:ob_end) = out_hess(net.nin+1,1:net.nin);
+hdata(ob_start:ob_end, b_index) = out_hess(1:net.nin, net.nin+1);
+
+return