On February 10th, Alessio Benavoli presented his recent work entitled ‘A unified framework for closed-form nonparametric regression, classification, preference, and mixed problems with Skew Gaussian Processes’. An abstract of Alessio’s talk is available below.
Gaussian Processes (GPs) are powerful nonparametric distributions over functions. For real-valued outputs, we can combine the GP prior with a Gaussian likelihood and perform exact posterior inference in closed form. However, in other cases, such as classification, preference learning, ordinal regression and mixed problems, the likelihood is no longer conjugate to the GP prior and closed-form expression for the posterior is not available. In this talk, I will show that is possible to derive closed-form expression for the posterior process in all the above cases (not only for regression), and that the posterior process is a Skew Gaussian Process (SkewGP). In the first part of the talk, I will give a brief introduction to GPs for nonparametric nonlinear regression. I will then move to SkewGPs to deal with nonlinear classification and preference learning problems. I will then discuss how SkewGPs can be used as surrogated model in Bayesian Optimisation and present an application to smart manufacturing. Finally, I will give an overview of my current research on this and other topics.
The code for the implementation of the method is available on Github.