Non-Gaussian Process Regression

Yaman Kindap, Simon J. Godsill

Keywords: Non-parametric regression, Bayesian methods, Approximate Inference, Levy processes

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.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

Submission Guidelines: Yes

Please Choose The Closest Area That Your Submission Falls Into: Probabilistic Methods (eg, variational inference, causal inference, Gaussian processes)

TL;DR: We extend the Gaussian process regression model to allow for locally adaptive behaviour through time-changed GPs and learn latent probabilistic representations of inputs.