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.
Regression GUI - initial stage
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.
Regression GUI - hyperparameter adaptation
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:
1D regression - sufficient data
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. ).
1D regression - pos.exp noise and pos.exp lik.
1D regression - pos.exp noise and pos.exp lik.

Questions, comments, suggestions: contact Lehel Csató.