Non-Gaussian Process Regression
This addresses the issue of inadequate uncertainty modeling in non-Gaussian datasets for users of Gaussian processes, representing a novel method for a known bottleneck rather than an incremental improvement.
The authors tackled the problem of standard Gaussian processes (GPs) failing to model uncertainty adequately in real-world datasets with non-Gaussian behaviors like heavy tails, by extending the GP framework to a new class of time-changed GPs that retain tractability. They demonstrated potential benefits compared to standard GPs, though no concrete numbers were provided in the abstract.
Standard GPs offer a flexible modelling tool for well-behaved processes. However, deviations from Gaussianity are expected to appear in real world datasets, with structural outliers and shocks routinely observed. In these cases GPs can fail to model uncertainty adequately and may over-smooth inferences. Here we extend the GP framework into a new class of time-changed GPs that allow for straightforward modelling of heavy-tailed non-Gaussian behaviours, while retaining a tractable conditional GP structure through an infinite mixture of non-homogeneous GPs representation. The conditional GP structure is obtained by conditioning the observations on a latent transformed input space and the random evolution of the latent transformation is modelled using a Lévy process which allows Bayesian inference in both the posterior predictive density and the latent transformation function. We present Markov chain Monte Carlo inference procedures for this model and demonstrate the potential benefits compared to a standard GP.