Distribution regression for sequential data

Conference item

Distribution regression refers to the supervised learning problem where labels are only available for groups of inputs instead of individual inputs. In this paper, we develop a rigorous mathematical framework for distribution regression where inputs are complex data streams. Leveraging properties of the expected signature and a recent signature kernel trick for sequential data from stochastic analysis, we introduce two new learning techniques, one feature-based and the other kernel-based. Each is suited to a different data regime in terms of the number of data streams and the dimensionality of the individual streams. We provide theoretical results on the universality of both approaches and demonstrate empirically their robustness to irregularly sampled multivariate time-series, achieving state-of-the-art performance on both synthetic and real-world examples from thermodynamics, mathematical finance and agricultural science.

Authors: Lemercier, M; Salvi, C; Damoulas, T; Bonilla, EV; Lyons, T

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Journal of Machine Learning Research
• Host title: Proceedings of The 24th International Conference on Artificial Intelligence and Statistics
• Pages: 3754-3762
• Series: Proceedings of Machine Learning Research
• Series number: 130
• Publication date: 2021-03-18
• Acceptance date: 2021-01-23
• Event title: 24th International Conference on Artificial Intelligence and Statistics (AISTATS 2021)
• Event location: Virtual event
• Event website: https://aistats.org/aistats2021/
• Event start date: 2021-04-13
• Event end date: 2021-04-15
• ISSN: 2640-3498
• Language: English