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1 function [h, hdata] = glmhess_weighted(net, x, t, eso_w, hdata)
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2 %GLMHESS Evaluate the Hessian matrix for a generalised linear model.
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3 %
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4 % Description
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5 % H = GLMHESS(NET, X, T) takes a GLM network data structure NET, a
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6 % matrix X of input values, and a matrix T of target values and returns
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7 % the full Hessian matrix H corresponding to the second derivatives of
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8 % the negative log posterior distribution, evaluated for the current
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9 % weight and bias values as defined by NET. Note that the target data
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10 % is not required in the calculation, but is included to make the
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11 % interface uniform with NETHESS. For linear and logistic outputs, the
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12 % computation is very simple and is done (in effect) in one line in
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13 % GLMTRAIN.
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14 %
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15 % See also
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16 % GLM, GLMTRAIN, HESSCHEK, NETHESS
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17 %
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18 % Copyright (c) Ian T Nabney (1996-9)
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19
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20 % Check arguments for consistency
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21 errstring = consist(net, 'glm', x, t);
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22 if ~isempty(errstring);
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23 error(errstring);
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24 end
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25
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26 ndata = size(x, 1);
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27 nparams = net.nwts;
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28 nout = net.nout;
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29 p = glmfwd(net, x);
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30 inputs = [x ones(ndata, 1)];
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31
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32 if nargin == 4
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33 hdata = zeros(nparams); % Full Hessian matrix
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34 % Calculate data component of Hessian
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35 switch net.outfn
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36
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37 case 'softmax'
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38 bb_start = nparams - nout + 1; % Start of bias weights block
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39 ex_hess = zeros(nparams); % Contribution to Hessian from single example
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40 for m = 1:ndata
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41 X = x(m,:)'*x(m,:);
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42 a = diag(p(m,:))-((p(m,:)')*p(m,:));
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43 a=eso_w(m,1)*a;
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44 ex_hess(1:nparams-nout,1:nparams-nout) = kron(a, X);
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45 ex_hess(bb_start:nparams, bb_start:nparams) = a.*ones(net.nout, net.nout);
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46 temp = kron(a, x(m,:));
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47 ex_hess(bb_start:nparams, 1:nparams-nout) = temp;
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48 ex_hess(1:nparams-nout, bb_start:nparams) = temp';
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49 hdata = hdata + ex_hess;
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50 end
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51
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52 otherwise
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53 error(['Unknown activation function ', net.actfn]);
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54 end
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55 end
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56
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57 [h, hdata] = hbayes(net, hdata);
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