wolffd@0: function g = mdngrad(net, x, t)
wolffd@0: %MDNGRAD Evaluate gradient of error function for Mixture Density Network.
wolffd@0: %
wolffd@0: %	Description
wolffd@0: %	 G = MDNGRAD(NET, X, T) takes a mixture density network data
wolffd@0: %	structure NET, a matrix X of input vectors and a matrix T of target
wolffd@0: %	vectors, and evaluates the gradient G of the error function with
wolffd@0: %	respect to the network weights. The error function is negative log
wolffd@0: %	likelihood of the target data.  Each row of X corresponds to one
wolffd@0: %	input vector and each row of T corresponds to one target vector.
wolffd@0: %
wolffd@0: %	See also
wolffd@0: %	MDN, MDNFWD, MDNERR, MDNPROB, MLPBKP
wolffd@0: %
wolffd@0: 
wolffd@0: %	Copyright (c) Ian T Nabney (1996-2001)
wolffd@0: %	David J Evans (1998)
wolffd@0: 
wolffd@0: % Check arguments for consistency
wolffd@0: errstring = consist(net, 'mdn', x, t);
wolffd@0: if ~isempty(errstring)
wolffd@0:   error(errstring);
wolffd@0: end
wolffd@0: 
wolffd@0: [mixparams, y, z] = mdnfwd(net, x);
wolffd@0: 
wolffd@0: % Compute gradients at MLP outputs: put the answer in deltas
wolffd@0: ncentres = net.mdnmixes.ncentres;
wolffd@0: dim_target = net.mdnmixes.dim_target;
wolffd@0: nmixparams = net.mdnmixes.nparams;
wolffd@0: ntarget = size(t, 1);
wolffd@0: deltas = zeros(ntarget, net.mlp.nout);
wolffd@0: e = ones(ncentres, 1);
wolffd@0: f = ones(1, dim_target);
wolffd@0: 
wolffd@0: post = mdnpost(mixparams, t);
wolffd@0: 
wolffd@0: % Calculate prior derivatives
wolffd@0: deltas(:,1:ncentres)  = mixparams.mixcoeffs - post;
wolffd@0: 
wolffd@0: % Calculate centre derivatives
wolffd@0: long_t = kron(ones(1, ncentres), t);
wolffd@0: centre_err = mixparams.centres - long_t;
wolffd@0: 
wolffd@0: % Get the post to match each u_jk:
wolffd@0: % this array will be (ntarget, (ncentres*dim_target))
wolffd@0: long_post = kron(ones(dim_target, 1), post);
wolffd@0: long_post = reshape(long_post, ntarget, (ncentres*dim_target));
wolffd@0: 
wolffd@0: % Get the variance to match each u_jk:
wolffd@0: var = mixparams.covars;
wolffd@0: var = kron(ones(dim_target, 1), var);
wolffd@0: var = reshape(var, ntarget, (ncentres*dim_target));
wolffd@0: 
wolffd@0: % Compute centre deltas
wolffd@0: deltas(:, (ncentres+1):(ncentres*(1+dim_target))) = ...
wolffd@0:                        (centre_err.*long_post)./var;
wolffd@0: 
wolffd@0: % Compute variance deltas
wolffd@0: dist2             = mdndist2(mixparams, t);
wolffd@0: c                 = dim_target*ones(ntarget, ncentres);
wolffd@0: deltas(:, (ncentres*(1+dim_target)+1):nmixparams) = ...
wolffd@0:                       post.*((dist2./mixparams.covars)-c)./(-2);
wolffd@0: 
wolffd@0: % Now back-propagate deltas through MLP
wolffd@0: g = mlpbkp(net.mlp, x, z, deltas);