25 research outputs found
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Time-warping invariants of multidimensional time series
In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, in a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly describe the data and to dampen the influence of noise. In some applications, these features are also required to satisfy some invariance properties. In this paper, we concentrate on time-warping invariants.We show that these correspond to a certain family of iterated sums of the increments of the time series, known as quasisymmetric functions in the mathematics literature. We present these invariant features in an algebraic framework, and we develop some of their basic properties
Time-warping invariants of multidimensional time series
In data science, one is often confronted with a time series representing
measurements of some quantity of interest. Usually, as a first step, features
of the time series need to be extracted. These are numerical quantities that
aim to succinctly describe the data and to dampen the influence of noise. In
some applications, these features are also required to satisfy some invariance
properties. In this paper, we concentrate on time-warping invariants. We show
that these correspond to a certain family of iterated sums of the increments of
the time series, known as quasisymmetric functions in the mathematics
literature. We present these invariant features in an algebraic framework, and
we develop some of their basic properties.Comment: 18 pages, 1 figur
Time-warping invariants of multidimensional time series
In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, in a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly describe the data and to dampen the influence of noise. In some applications, these features are also required to satisfy some invariance properties. In this paper, we concentrate on time-warping invariants.We show that these correspond to a certain family of iterated sums of the increments of the time series, known as quasisymmetric functions in the mathematics literature. We present these invariant features in an algebraic framework, and we develop some of their basic properties
Tropical time series, iterated-sum signatures and quasisymmetric functions
Driven by the need for principled extraction of features from time series, we introduce the iterated-sums signature over any commutative semiring. The case of the tropical semiring is a central, and our motivating, example, as it leads to features of (real-valued) time series that are not easily available using existing signature-type objects
Tropical time series, iterated-sums signatures and quasisymmetric functions
Driven by the need for principled extraction of features from time series, we
introduce the iterated-sums signature over any commutative semiring. The case
of the tropical semiring is a central, and our motivating, example, as it leads
to features of (real-valued) time series that are not easily available using
existing signature-type objects.Comment: fix notational errors, clarify certain proof
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Stability of deep neural networks via discrete rough paths
Using rough path techniques, we provide a priori estimates for the output of Deep Residual Neural Networks. In particular we derive stability bounds in terms of the total p-variation of trained weights for any p ≥ 1
Stability of deep neural networks via discrete rough paths
Using rough path techniques, we provide a priori estimates for the output of Deep Residual Neural Networks. In particular we derive stability bounds in terms of the total p-variation of trained weights for any p ≥ 1
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Iterated-sums signature, quasi-symmetric functions and time series analysis
We survey and extend results on a recently defined character on the quasi-shuffle algebra. This character, termed iterated-sums signature, appears in the context of time series analysis and originates from a problem in dynamic time warping. Algebraically, it relates to (multidimensional) quasisymmetric functions as well as (deformed) quasi-shuffle algebras
Automorphisms of the universal enveloping algebra of a finite-dimensional Zinbiel algebra with zero multiplication
In recent years there has been a great interest in the study of Zinbiel (dual Leibniz) algebras. Let A be Zinbiel algebra over an arbitrary field K and let e1,e2,...,em,... be a linear basis of A. In 2010 A. Naurazbekova, using the methods of Gro¨bner-Shirshov bases, constructed the basis of the universal (multiplicative) enveloping algebra U(A) of A. Using this result, the automorphisms of the universal enveloping algebra of a finite-dimensional Zinbiel algebra with zero multiplication are described