Learning non-Gaussian Time Series using the Box-Cox Gaussian Process

TL;DR

This paper introduces a novel approach for modeling non-Gaussian time series using Gaussian processes with a Box-Cox warping, optimizing training with derivative-free methods and enabling analytical predictions.

Contribution

It proposes a Box-Cox based warping function for GPs and a derivative-free optimization method to improve training and prediction efficiency for non-Gaussian data.

Findings

Predictions can be computed analytically.

The method effectively models real-world non-Gaussian time series.

Improved training stability and computational efficiency.

Abstract

Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model general non-Gaussian data with complex correlation structure, GPs can be paired with an expressive covariance kernel and then fed into a nonlinear transformation (or warping). However, overparametrising the kernel and the warping is known to, respectively, hinder gradient-based training and make the predictions computationally expensive. We remedy this issue by (i) training the model using derivative-free global-optimisation techniques so as to find meaningful maxima of the model likelihood, and (ii) proposing a warping function based on the celebrated Box-Cox transformation that requires minimal numerical approximations---unlike existing warped GP models. We validate the proposed approach by first showing that predictions can be computed analytically, and then on a learning, reconstruction and forecasting experiment using real-world datasets.