Related papers: Insertion algorithm for inverting the signature of…

We establish a universal approximation theorem for signatures of rough paths that are not necessarily weakly geometric. By extending the path with time and its rough path bracket terms, we prove that linear functionals of the signature of…

We characterize the signature of piecewise continuously differentiable paths transformed by a polynomial map in terms of the signature of the original path. For this aim, we define recursively an algebra homomorphism between two shuffle…

Modern computer vision algorithms have brought significant advancement to 3D geometry reconstruction. However, illumination and material reconstruction remain less studied, with current approaches assuming very simplified models for…

Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…

Neural network systems describe complex mappings that can be very difficult to understand. In this paper, we study the inverse problem of determining the input images that get mapped to specific neural network classes. Ultimately, we expect…

We propose a new approach to circumvent the sign problem in which the integration path is optimized to control the sign problem. We give a trial function specifying the integration path in the complex plane and tune it to optimize the cost…

The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis. It is here examined through the lens of algebraic geometry.…

We study nonparametric regression and classification for path-valued data. We introduce a functional Nadaraya-Watson estimator that combines the signature transform from rough path theory with local kernel regression. The signature…

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 as a fixed feature transformation, on top of which a…

Signature tensors of paths are a versatile tool for data analysis and machine learning. Recently, they have been applied to persistent homology, by embedding barcodes into spaces of paths. Among the different path embeddings, the…

Inspired by the great success of recurrent neural networks (RNNs) in sequential modeling, we introduce a novel RNN system to improve the performance of online signature verification. The training objective is to directly minimize…

In this paper, we present an algorithm that enumerates a certain class of signed permutations, referred to as grid signed permutation classes. In the case of permutations, the corresponding grid classes are of interest because they are…

Computing the reversal distances of signed permutations is an important topic in Bioinformatics. Recently, a new lower bound for the reversal distance was obtained via the plane permutation framework. This lower bound appears different from…

Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…

We introduce the notions of tree-like path and tree-like equivalence between paths and prove that the latter is an equivalence relation for paths of finite length. We show that the equivalence classes form a group with some similarity to a…

We investigate the use of path signatures in a machine learning context for hedging exotic derivatives under non-Markovian stochastic volatility models. In a deep learning setting, we use signatures as features in feedforward neural…

This paper establishes a comprehensive concentration theory for truncated signatures of Gaussian rough paths. The signature of a path, defined as the collection of all iterated integrals, provides a complete description of its geometric…

Splines are central objects for the interpolation of discrete data via piecewise smooth paths. Their iterated-integral signature is an infinite collection of tensors which characterizes paths almost uniquely. We study truncations of this…

Over the past decade, the importance of the 1D signature which can be seen as a functional defined along a path, has been pivotal in both path-wise stochastic calculus and the analysis of time series data. By considering an image as a…

In this paper, we introduce the branched signature model, motivated by the branched rough path framework of [Gubinelli, Journal of Differential Equations, 248(4), 2010], which generalizes the classical geometric rough path. We establish a…