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1 function g = mdngrad(net, x, t)
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2 %MDNGRAD Evaluate gradient of error function for Mixture Density Network.
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3 %
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4 % Description
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5 % G = MDNGRAD(NET, X, T) takes a mixture density network data
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6 % structure NET, a matrix X of input vectors and a matrix T of target
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7 % vectors, and evaluates the gradient G of the error function with
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8 % respect to the network weights. The error function is negative log
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9 % likelihood of the target data. Each row of X corresponds to one
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10 % input vector and each row of T corresponds to one target vector.
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11 %
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12 % See also
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13 % MDN, MDNFWD, MDNERR, MDNPROB, MLPBKP
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14 %
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15
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16 % Copyright (c) Ian T Nabney (1996-2001)
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17 % David J Evans (1998)
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18
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19 % Check arguments for consistency
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20 errstring = consist(net, 'mdn', x, t);
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21 if ~isempty(errstring)
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22 error(errstring);
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23 end
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24
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25 [mixparams, y, z] = mdnfwd(net, x);
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26
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27 % Compute gradients at MLP outputs: put the answer in deltas
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28 ncentres = net.mdnmixes.ncentres;
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29 dim_target = net.mdnmixes.dim_target;
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30 nmixparams = net.mdnmixes.nparams;
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31 ntarget = size(t, 1);
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32 deltas = zeros(ntarget, net.mlp.nout);
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33 e = ones(ncentres, 1);
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34 f = ones(1, dim_target);
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35
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36 post = mdnpost(mixparams, t);
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37
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38 % Calculate prior derivatives
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39 deltas(:,1:ncentres) = mixparams.mixcoeffs - post;
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40
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41 % Calculate centre derivatives
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42 long_t = kron(ones(1, ncentres), t);
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43 centre_err = mixparams.centres - long_t;
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44
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45 % Get the post to match each u_jk:
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46 % this array will be (ntarget, (ncentres*dim_target))
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47 long_post = kron(ones(dim_target, 1), post);
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48 long_post = reshape(long_post, ntarget, (ncentres*dim_target));
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49
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50 % Get the variance to match each u_jk:
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51 var = mixparams.covars;
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52 var = kron(ones(dim_target, 1), var);
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53 var = reshape(var, ntarget, (ncentres*dim_target));
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54
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55 % Compute centre deltas
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56 deltas(:, (ncentres+1):(ncentres*(1+dim_target))) = ...
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57 (centre_err.*long_post)./var;
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58
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59 % Compute variance deltas
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60 dist2 = mdndist2(mixparams, t);
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61 c = dim_target*ones(ntarget, ncentres);
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62 deltas(:, (ncentres*(1+dim_target)+1):nmixparams) = ...
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63 post.*((dist2./mixparams.covars)-c)./(-2);
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64
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65 % Now back-propagate deltas through MLP
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66 g = mlpbkp(net.mlp, x, z, deltas);
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