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• W3034907790 abstract "We introduce a learning framework to infer macroscopic properties of an evolving system from longitudinal trajectories of its components. By considering probability measures on continuous paths we view this problem as a distribution regression task for continuous-time processes and propose two distinct solutions leveraging the recently established properties of the expected signature. Firstly, we embed the measures in a Hilbert space, enabling the application of an existing kernel-based technique. Secondly, we recast the complex task of learning a non-linear regression function on probability measures to a simpler functional linear regression on the signature of a single vector-valued path. We provide theoretical results on the universality of both approaches, and demonstrate empirically their robustness to densely and irregularly sampled multivariate time-series, outperforming existing methods adapted to this task on both synthetic and real-world examples from thermodynamics, mathematical finance and agricultural science." @default.
• W3034907790 created "2020-06-19" @default.
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• W3034907790 date "2020-06-10" @default.
• W3034907790 modified "2023-09-27" @default.
• W3034907790 title "Distribution Regression for Continuous-Time Processes via the Expected Signature." @default.
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• W3034907790 hasPublicationYear "2020" @default.
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