Deep signature transforms

P Kidger, P Bonnier, I Perez Arribas… - Advances in neural …, 2019‏ - proceedings.neurips.cc
The signature is an infinite graded sequence of statistics known to characterise a stream of
data up to a negligible equivalence class. It is a transform which has previously been treated …

Embedding and learning with signatures

A Fermanian - Computational Statistics & Data Analysis, 2021‏ - Elsevier
Sequential and temporal data arise in many fields of research, such as quantitative finance,
medicine, or computer vision. A novel approach for sequential learning, called the signature …

Deep signature transforms

P Bonnier, P Kidger, IP Arribas, C Salvi… - arxiv preprint arxiv …, 2019‏ - arxiv.org
The signature is an infinite graded sequence of statistics known to characterise a stream of
data up to a negligible equivalence class. It is a transform which has previously been treated …

Inverting the signature of a path

TJ Lyons, W Xu - Journal of the European Mathematical Society, 2018‏ - ems.press
Inverting the signature of a path Page 1 DOI 10.4171/JEMS/796 J. Eur. Math. Soc. 20, 1655–1687
c European Mathematical Society 2018 Terry J. Lyons · Weijun Xu Inverting the signature of a …

Controlled differential equations on long sequences via non-standard wavelets

S Pal, Z Zeng, SN Ravi, V Singh - … Conference on Machine …, 2023‏ - proceedings.mlr.press
Abstract Neural Controlled Differential equations (NCDE) are a powerful mechanism to
model the dynamics in temporal sequences, eg, applications involving physiological …

The insertion method to invert the signature of a path

A Fermanian, J Chang, T Lyons, G Biau - Recent Advances in …, 2024‏ - Springer
The signature is a representation of a path as an infinite sequence of its iterated integrals.
Under certain assumptions, the signature characterizes the path, up to translation and …

Insertion algorithm for inverting the signature of a path

J Chang, T Lyons - arxiv preprint arxiv:1907.08423, 2019‏ - arxiv.org
In this article we introduce the insertion method for reconstructing the path from its signature,
ie inverting the signature of a path. For this purpose, we prove that a converging upper …

Path signatures on Lie groups

D Lee, R Ghrist - arxiv preprint arxiv:2007.06633, 2020‏ - arxiv.org
Path signatures are powerful nonparametric tools for time series analysis, shown to form a
universal and characteristic feature map for Euclidean valued time series data. We lift the …

Expected signature on a Riemannian manifold and its geometric implications

X Geng, H Ni, C Wang - arxiv preprint arxiv:2407.13086, 2024‏ - arxiv.org
On a compact Riemannian manifold $ M, $ we show that the Riemannian distance function $
d (x, y) $ can be explicitly reconstructed from suitable asymptotics of the expected signature …

Introduction to rough paths theory

MG Varzaneh, S Riedel - arxiv preprint arxiv:2302.04653, 2023‏ - arxiv.org
These notes are an extended version of the course" Introduction to rough paths theory"
given at the XXV Brazilian School of Probability in Campinas in August 2022. Their aim is to …