Learning non-Gaussian Time Series using the Box-Cox Gaussian Process
This work addresses the problem of efficiently modeling complex non-Gaussian data for researchers and practitioners in time series analysis, though it is incremental as it builds on existing warped GP models with specific optimizations.
The paper tackles the challenge of modeling non-Gaussian time series with Gaussian processes by addressing overparameterization and computational inefficiencies in existing methods. It proposes using derivative-free optimization and a Box-Cox transformation-based warping function, validated through analytical predictions and experiments on real-world datasets, showing improved performance in learning, reconstruction, and forecasting tasks.
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.