SigGPDE: scaling sparse Gaussian Processes on sequential data

Conference item

Making predictions and quantifying their uncertainty when the input data is sequential is a fundamental learning challenge, recently attracting increasing attention. We develop SigGPDE, a new scalable sparse variational inference framework for Gaussian Processes (GPs) on sequential data. Our contribution is twofold. First, we construct inducing variables underpinning the sparse approximation so that the resulting evidence lower bound (ELBO) does not require any matrix inversion. Second, we show that the gradients of the GP signature kernel are solutions of a hyperbolic partial differential equation (PDE). This theoretical insight allows us to build an efficient back-propagation algorithm to optimize the ELBO. We showcase the significant computational gains of SigGPDE compared to existing methods, while achieving state-of-the-art performance for classification tasks on large datasets of up to 1 million multivariate time series.

Authors: Lemercier, M; Salvi, C; Cass, T; Bonilla, EV; Damonlas, T

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Journal of Machine Learning Research
• Host title: Proceedings of the 38th International Conference on Machine Learning
• Pages: 6233-6242
• Series: Proceedings of Machine Learning Research
• Series number: 139
• Publication date: 2021-07-24
• Acceptance date: 2021-05-08
• Event title: 38th International Conference on Machine Learning (ICML 2021)
• Event series: International Conference on Machine Learning
• Event location: Virtual
• Event website: https://icml.cc/
• Event start date: 2021-07-18
• Event end date: 2021-07-24
• ISSN: 2640-3498
• Language: English