Efficient and scalable inference for generalized student - T process models

Abstract

Gaussian Processes are a popular, nonparametric modelling framework for solving a wide range of regression problems. However, they are suffering from 2 major shortcomings. On the one hand, they require efficient, approximate inference for non-Gaussian observation likelihoods (the Generalized Gaussian Process Regression problem) and, on they other hand, their cubic run time in the number of observations is a major obstacle to large-scale inference tasks.

In recent years, the development of efficient and scalable inference methods for the Gen- eralized Gaussian Process Regression problem has progressed steadily. However, the more robust generalization of the Gaussian Process, the Student-t Process, while suffering under the same shortcomings, has not been given the same amount of attention with respect to more general likelihoods.

In this thesis, we utilize the mathematical framework of q-algebra to extend some of the efficient and scalable methods for Generalized Gaussian Process Regression to the case of Generalized Student-t Process Regression.

We demonstrate in experiments that some of our Student-t based methods can compete with their Gaussian counterparts and that they can be be more robust to mislabelled data. However, we also see that the new methods are suffering under severe convergence problems and need considerable effort to tune them properly.