From the 1 of 6 linked papers with an AI index.
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
The paper introduces signature controlled differential equations (Sig‑CDEs) and shows that they can universally approximate any well‑posed path‑dependent controlled differential eq…
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…
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…
Expected Signature Kernels for Lévy Rough Paths
Peter K. Friz, Paul P. Hager
The expected signature kernel arises in statistical learning tasks as a similarity measure of probability measures on path space. Computing this kernel for known classes of stochas…
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…