Thesis defense Luca Ambrogioni (Donders series 387)

6 June 2019

Gaussian Processes and Beyond: From Dynamical: Modeling to Statistical Signal Processing

The thesis is divided in three main parts. The first two parts are based on the framework of Gaussian process regression. What distinguishes the methods proposed in the first part from the methods introduced in the second parts is the logic behind the choice of the functional priors. The methods presented in the first part are based on informative priors derived from dynamical models and stochastic differential equations. This allows to construct functional priors that are tailored to some specific neural systems. Conversely, the second part is devoted to the Bayesian reformulation of signal processing methods. The inflectional priors in this second part are designed to be as uninformative as possible so that the same method can be directly applied to any kind of time series. Finally, in the third part of the thesis I will introduce two methods for going beyond the requirement of Gaussianity and therefore outside of the realm of Gaussian process regression.