Likelihood initialisation for the Online Gaussian Process structure.
ogpinit(net, likfn, likpar,likoptfn)
ogpinit(likfn, likpar) uses the GLOBAL structure net of an
online Gaussian Process data structure net and sets the
function (net.likfn) that returns the online update coefficients. The
vector net.likpar sets the additional parameters to this function.
With three arguments: ogpinit(likfn,likpar,likoptfn), the
third argument is the address of the optimiser to the likelihood parameter.
The optimiser assumes that there exists an approximation to the posterior
process and the values of the posterior mean and variance at the training
locations are available. The optimisation of the likelihood parameters is
independent of the optimisation of the covariance kernel parameters.
If the third argument in calling ogpinit or the field
net.likoptfn is empty then there is no likelihood parameter
optimisation in the function ogptrain.
Below there is a description of the functions and parameters involved in likelihood optimsation.
The address in likfn is to a function that computes the coefficients
for the online learning.
[loglik, q, r] = likfn(likpar, y, mu, var, mu_p, var_p);
with the following parameters:
likpar - the likelihood parameter (see eg. c_reg_gauss).
y- the training (noisy) outputs at the input.
mu, var- the predicted mean and variance (i.e. the statistics of the marginal GP at the input).
mu_p, var_p - the values of the prior mean and variance
before the addition of the new data - called cavity means and variances.
Providing these values is optional and it is returned by ogppost within
the structure gpopt.
loglik- the value of the log-average.
q, r - the update coeficients to the online learning
algorithm - vector and matrix of size nout (see c_reg_gauss).
The function likoptfn has the following structure:
newlikpar = likoptfn(oldlikpar, y, cavM, cavV, postM, postV);
where the input and output parameters are the following:
newlikpar, oldlikpar- the new and old values of the likelihood parameters.
y- the vector of training inputs
cavM, cavV- vector of prior means and variances corresponding to the training locations !! AND !! with the contribution of the current input removed (cavity parameters).
postM, postV- (optional) vector of posteior means and variances which is sometimes needed, e.g. if one wants to use the EM algorithm.
ogp, ogptrain, c_reg_gauss, c_reg_exp, em_gauss, em_lapl
Copyright (c) Lehel Csató (2001-2004)