Sparse OGP Regression
In the example program
demogp_reg_gui
,
one can generate noisy realisations of the
sinc
function. The noise is always assumed to be additive but its type and
amplitude can be set manually together with other model parameters.
Although there are initial values for the hyperparameters, the optimal
values can be learnt using evidence maximisation. The
figures below show examples of how the parameter selection works.
The regression demo
demogp_reg
is a
script which can be used to start coding using the package.
Figure 1. Using the default settings and generating 40 training points, the
result of learning (before the hyper-parameter adaptation) is
visualised in the image below.
Figure 2. The feature of the OGP package (and the
approximations) is that it allows the estimation of hyperparameters
(the yellow button HYP L.).
For this toy example one has:
Figure 3. A final picture for the Gaussian example, if there
are many training inputs, then one can estimate the true
latent function accurately, this is shown by the tighter predictive error bars (thin red lines) around
the mean function of the GP.
The above example is for Gaussian additive noise and gaussian
likelihood. Using the same GUI demogp_reg_gui
, one has
the possibility to generate the true noise from other distributions,
like symmetric Laplace or an exponential-type noise with only positive
values. Below two examples are shown where the noise type is positive
exponential and for the inference we assumed the correct positive
exponential noise, shown on Fig.4, and Gaussian noise
respectively (Fig. 5. ).
Questions, comments, suggestions: contact Lehel
Csató.