Generalized iterated-sums signatures
نویسندگان
چکیده
We explore the algebraic properties of a generalized version iterated-sums signature, inspired by previous work F. Király and H. Oberhauser. In particular, we show how to recover character property associated linear map on tensor algebra considering deformed quasi-shuffle product words. introduce three non-linear transformations signatures, close in spirit Machine Learning applications, some their properties.
منابع مشابه
Persistence of iterated partial sums
Let S (2) n denote the iterated partial sums. That is, S (2) n = S1 + S2 + · · · + Sn, where Si = X1+X2+ · · ·+Xi. Assuming X1, X2, . . . , Xn are integrable, zero-mean, i.i.d. random variables, we show that the persistence probabilities p n := P ( max 1≤i≤n S (2) i < 0 ) ≤ c √ E|Sn+1| (n+ 1)E|X1| , with c ≤ 6 √ 30 (and c = 2 wheneverX1 is symmetric). Furthermore, the converse inequality holds ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2023
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2023.06.007