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function [h, hdata] = glmhess_weighted(net, x, t, eso_w, 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.
%
% See also
% GLM, GLMTRAIN, HESSCHEK, NETHESS
%
% Copyright (c) Ian T Nabney (1996-9)
% 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 == 4
hdata = zeros(nparams); % Full Hessian matrix
% Calculate data component of Hessian
switch net.outfn
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,:));
a=eso_w(m,1)*a;
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.actfn]);
end
end
[h, hdata] = hbayes(net, hdata);
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