gpPosteriorGradMeanVar.m

function [gmu, gsigmavar] = gpPosteriorGradMeanVar(model, X);

% GPPOSTERIORGRADMEANVAR Gadient of the mean and variances of the posterior at points given by X.
% FORMAT
% DESC computes the gradient of the mean and variances of the
% posterior distribution of a Gaussian process with respect to the
% input locations.
% ARG model : the model for which gradients are to be computed.
% ARG X : the input locations where gradients are to be computed.
% RETURN gmu : the gradient of the posterior mean with respect to
% the input locations.
% RETURN gsigmavar : the gradient of the posterior variances with
% respect to the input locations.
%
% SEEALSO : gpCreate, gpPosteriorMeanVar
%
% COPYRIGHT : Neil D. Lawrence, 2005, 2006, 2009

% GP


if ~isfield(model, 'alpha')
  model = gpComputeAlpha(model);
end

if size(X, 1) > 1
  error('This function only handles one data-point at a time')
end

switch model.approx
 case 'ftc'
  gX = kernGradX(model.kern, X, model.X);
  kX = kernCompute(model.kern, X, model.X)';
 case {'dtc', 'dtcvar', 'fitc', 'pitc'}
  gX = kernGradX(model.kern, X, model.X_u);
  kX = kernCompute(model.kern, X, model.X_u)';
 otherwise
  error('Unrecognised approximation type');
end

diaggK = kernDiagGradX(model.kern, X);

gmu = zeros(size(X, 2), model.d);
gsigmavar = zeros(size(X, 2), model.d);

switch model.approx
 case 'ftc'
  Kinvgk = model.invK_uu*gX;
 case {'dtc', 'dtcvar', 'fitc', 'pitc'}
  Kinvgk = (model.invK_uu - (1/model.beta)*model.Ainv)*gX;
 otherwise
  error('Unrecognised approximation type');
end

gsigmavar = repmat(diaggK' - 2*Kinvgk'*kX, 1, model.d);
gmu = gX'*model.alpha;

gmu = gmu.*repmat(model.scale, model.q, 1);
gsigmavar = gsigmavar.*repmat(model.scale.*model.scale, model.q, 1);