6 papers
Expected signatures via partial integration, coordinate change and symmetrization
Paul P. Hager, Luca Pelizzari
We study signature transformations of heterogeneous paths whose components may differ in regularity and probabilistic structure. We introduce an invertible change of coor…
Dynamic Universal Approximation via Signature Controlled Differential Equations
Tomás Carrondo, Christa Cuchiero, Paul P. Hager +1
We study signature controlled differential equations (Sig-CDEs), that is, path-dependent controlled differential equations (CDEs) whose vector fields factor through the signature m…
Computational aspects of the Volterra Signature
Paul P. Hager, Fabian N. Harang, Luca Pelizzari +1
The Volterra signature extends the classical path signature by incorporating general matrix-valued kernel into its iterated integral structure, yielding a flexible notion of memory…
The Volterra signature
Paul P. Hager, Fabian N. Harang, Luca Pelizzari +1
Modern approaches for learning from non-Markovian time series, such as recurrent neural networks, neural controlled differential equations or transformers, typically rely on implic…
Expected Signature Kernels for Rough Paths
Peter K. Friz, Paul P. Hager
The expected signature kernel is a similarity measure of probability laws on path space and enters directly into signature maximum mean discrepancies. Building on [P. K. Friz, P. P…
On expected signatures and signature cumulants in semimartingale models
Peter K. Friz, Paul P. Hager, Nikolas Tapia
The concept of signatures and expected signatures is vital in data science, especially for sequential data analysis. The signature transform, a Cartan type development, translates…