Related papers: Signatures in Shape Analysis: an Efficient Approac…
Understanding protein dynamics are essential for deciphering protein functional mechanisms and developing molecular therapies. However, the complex high-dimensional dynamics and interatomic interactions of biological processes pose…
In this work we investigate the use of the Signature Transform in the context of Learning. Under this assumption, we advance a supervised framework that potentially provides state-of-the-art classification accuracy with the use of few…
Geometric features, robust to noise, of curves in Euclidean space are of great interest for various applications such as machine learning and image analysis. We apply the Fels-Olver's moving frame method (for geometric features) paired with…
The signature of a rectifiable path is a tensor series in the tensor algebra whose coefficients are definite iterated integrals of the path. The signature characterises the path up to a generalised form of reparametrisation. It is a…
The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors at a particular level gives rise to the universal signature…
We suggest a purely combinatorial approach to a general problem in system reliability. We show how to determine if a given vector can be the signature of a system, and in the affirmative case exhibit such a system in terms on its structure…
Statistical classification of actions in videos is mostly performed by extracting relevant features, particularly covariance features, from image frames and studying time series associated with temporal evolutions of these features. A…
Iterated-integral signatures and log signatures are vectors calculated from a path that characterise its shape. They come from the theory of differential equations driven by rough paths, and also have applications in statistics and machine…
Signature verification has been one of the major researched areas in the field of computer vision. Many financial and legal organizations use signature verification as access control and authentication. Signature images are not rich in…
Over-parameterized deep models usually over-fit to a given training distribution, which makes them sensitive to small changes and out-of-distribution samples at inference time, leading to low generalization performance. To this end, several…
The aim of this article is to provide a simple sampling procedure to reconstruct any monotone path from its signature. For every N, we sample a lattice path of N steps with weights given by the coefficient of the corresponding word in the…
Deep hedging is a promising direction in quantitative finance, incorporating models and techniques from deep learning research. While giving excellent hedging strategies, models inherently requires careful treatment in designing…
We introduce the notion of property signatures, a representation for programs and program specifications meant for consumption by machine learning algorithms. Given a function with input type $\tau_{in}$ and output type $\tau_{out}$, a…
This paper focuses on the mathematical framework for reducing the complexity of models using path signatures. The structure of these signatures, which can be interpreted as collections of iterated integrals along paths, is discussed and…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
In this article we introduce the insertion method for reconstructing the path from its signature, i.e. inverting the signature of a path. For this purpose, we prove that a converging upper bound exists for the difference between the…
We define a characteristic function for probability measures on the signatures of geometric rough paths. We determine sufficient conditions under which a random variable is uniquely determined by its expected signature, thus partially…
In the context of controlled differential equations, the signature is the exponential function on paths. B. Hambly and T. Lyons proved that the signature of a bounded variation path is trivial if and only if the path is tree-like. We extend…
Document digitization is becoming increasingly crucial. In this work, we propose a shape based approach for automatic stamp verification/detection in document images using an unsupervised feature learning. Given a small set of training…
In this paper, we propose a novel set of features for offline writer identification based on the path signature approach, which provides a principled way to express information contained in a path. By extracting local pathlets from…