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1 function [extra, invhess] = fevbayes(net, y, a, x, t, x_test, invhess)
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2 %FEVBAYES Evaluate Bayesian regularisation for network forward propagation.
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3 %
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4 % Description
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5 % EXTRA = FEVBAYES(NET, Y, A, X, T, X_TEST) takes a network data
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6 % structure NET together with a set of hidden unit activations A from
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7 % test inputs X_TEST, training data inputs X and T and outputs a matrix
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8 % of extra information EXTRA that consists of error bars (variance) for
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9 % a regression problem or moderated outputs for a classification
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10 % problem. The optional argument (and return value) INVHESS is the
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11 % inverse of the network Hessian computed on the training data inputs
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12 % and targets. Passing it in avoids recomputing it, which can be a
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13 % significant saving for large training sets.
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14 %
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15 % This is called by network-specific functions such as MLPEVFWD which
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16 % are needed since the return values (predictions and hidden unit
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17 % activations) for different network types are in different orders (for
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18 % good reasons).
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19 %
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20 % See also
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21 % MLPEVFWD, RBFEVFWD, GLMEVFWD
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22 %
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23
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24 % Copyright (c) Ian T Nabney (1996-2001)
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25
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26 w = netpak(net);
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27 g = netderiv(w, net, x_test);
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28 if nargin < 7
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29 % Need to compute inverse hessian
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30 hess = nethess(w, net, x, t);
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31 invhess = inv(hess);
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32 end
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33
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34 ntest = size(x_test, 1);
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35 var = zeros(ntest, 1);
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36 for idx = 1:1:net.nout,
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37 for n = 1:1:ntest,
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38 grad = squeeze(g(n,:,idx));
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39 var(n,idx) = grad*invhess*grad';
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40 end
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41 end
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42
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43 switch net.outfn
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44 case 'linear'
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45 % extra is variance
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46 extra = ones(size(var))./net.beta + var;
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47 case 'logistic'
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48 % extra is moderated output
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49 kappa = 1./(sqrt(ones(size(var)) + (pi.*var)./8));
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50 extra = 1./(1 + exp(-kappa.*a));
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51 case 'softmax'
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52 % Use extended Mackay formula; beware that this may not
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53 % be very accurate
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54 kappa = 1./(sqrt(ones(size(var)) + (pi.*var)./8));
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55 temp = exp(kappa.*a);
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56 extra = temp./(sum(temp, 2)*ones(1, net.nout));
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57 otherwise
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58 error(['Unknown activation function ', net.outfn]);
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59 end
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