A signature-based algorithm for solving an inverse problem with discretely observed trajectories of rough differential equations

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• Thomas Morrish (University of Warwick)
• Wednesday 04 September 2024, 15:30-15:50
• Seminar Room 1, Newton Institute.

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SSDW05 - Modelling and Applications of Anomalous Diffusions

Motivated by the challenge of constructing a likelihood for irregularly and discretely observed rough differential equations, pertinent for areas such as animal movement modelling, we introduce and study a novel algorithm, inspired by signatures, that aims to solve the dual problem of constructing a geometric p-rough path $X$ whose response $Y$ through a known model is consistent with the discrete observations $y$. Unlike local methods, the algorithm considers the entire trajectory at each iteration, uniformly controlling errors in p-variation. We consider its performance against a local algorithm across various modelling scenarios, including unobserved dimensions, varying driver roughness and sampling rates, and path dependence. The algorithm is designed to be consistent with any parameterisation and is straightforward to implement. Due to its flexibility, potential applications extend beyond animal movement modelling to fields such as computational biology, finance, and population genetics.

This talk is part of the Isaac Newton Institute Seminar Series series.

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