Generalized iterated-sums signatures
This work provides theoretical advancements in the algebraic understanding of iterated-sums signatures, which could be relevant for researchers working on time series analysis in machine learning.
This paper explores the algebraic properties of a generalized iterated-sums signature, recovering the character property of its associated linear map by using a deformed quasi-shuffle product. It also introduces three non-linear transformations on these signatures, relevant to Machine Learning applications.
We explore the algebraic properties of a generalized version of the iterated-sums signature, inspired by previous work of F.~Király and H.~Oberhauser. In particular, we show how to recover the character property of the associated linear map over the tensor algebra by considering a deformed quasi-shuffle product of words on the latter. We introduce three non-linear transformations on iterated-sums signatures, close in spirit to Machine Learning applications, and show some of their properties.