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Related papers: Expected Signature Kernels for L\'evy Rough Paths

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Process convolutions yield random fields with flexible marginal distributions and dependence beyond Gaussianity, but statistical inference is often hampered by a lack of closed-form marginal distributions, and simulation-based inference may…

Methodology · Statistics 2017-10-19 Thomas Opitz

Structural kernels are a flexible learning paradigm that has been widely used in Natural Language Processing. However, the problem of model selection in kernel-based methods is usually overlooked. Previous approaches mostly rely on setting…

Computation and Language · Computer Science 2015-08-11 Daniel Beck , Trevor Cohn , Christian Hardmeier , Lucia Specia

Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…

Machine Learning · Computer Science 2015-02-19 Rafael Boloix-Tortosa , F. Javier Payán-Somet , Eva Arias-de-Reyna , Juan José Murillo-Fuentes

In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…

Optimization and Control · Mathematics 2016-04-20 Martin Eigel , Kevin Sturm

Persistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discrete multisets of points in the plane $\mathbb{R}^2$ that can…

Computational Geometry · Computer Science 2019-03-25 Frédéric Chazal , Vincent Divol

We study pathwise invariances of centred random fields that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path properties including…

Statistics Theory · Mathematics 2013-08-07 David Ginsbourger , Olivier Roustant , Nicolas Durrande

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…

Probability · Mathematics 2026-02-06 Mihriban Ceylan , Anna P. Kwossek , David J. Prömel

Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of…

Machine Learning · Statistics 2016-06-03 Seth Flaxman , Dino Sejdinovic , John P. Cunningham , Sarah Filippi

Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time.…

Machine Learning · Statistics 2021-11-05 Cristopher Salvi , Maud Lemercier , Chong Liu , Blanka Hovarth , Theodoros Damoulas , Terry Lyons

Choosing a proper set of kernel functions is an important problem in learning Gaussian Process (GP) models since each kernel structure has different model complexity and data fitness. Recently, automatic kernel composition methods provide…

Machine Learning · Computer Science 2021-02-25 Anh Tong , Toan Tran , Hung Bui , Jaesik Choi

We consider Markov models of stochastic processes where the next-step conditional distribution is defined by a kernel density estimator (KDE), similar to Markov forecast densities and certain time-series bootstrap schemes. The KDE Markov…

Machine Learning · Computer Science 2018-07-31 Gustav Eje Henter , Arne Leijon , W. Bastiaan Kleijn

Traditional hidden Markov models have been a useful tool to understand and model stochastic dynamic data; in the case of non-Gaussian data, models such as mixture of Gaussian hidden Markov models can be used. However, these suffer from the…

Machine Learning · Statistics 2023-05-16 Carlos Puerto-Santana , Concha Bielza , Pedro Larrañaga , Gustav Eje Henter

In computational physics, machine learning has now emerged as a powerful complementary tool to explore efficiently candidate designs in engineering studies. Outputs in such supervised problems are signals defined on meshes, and a natural…

Machine Learning · Statistics 2025-03-11 Raphaël Carpintero Perez , Sébastien da Veiga , Josselin Garnier , Brian Staber

This paper proposes a physically consistent Gaussian Process (GP) enabling the identification of uncertain Lagrangian systems. The function space is tailored according to the energy components of the Lagrangian and the differential equation…

Machine Learning · Computer Science 2023-02-06 Giulio Evangelisti , Sandra Hirche

Standard GPs offer a flexible modelling tool for well-behaved processes. However, deviations from Gaussianity are expected to appear in real world datasets, with structural outliers and shocks routinely observed. In these cases GPs can fail…

Machine Learning · Statistics 2022-09-08 Yaman Kındap , Simon Godsill

When analyzing modern machine learning algorithms, we may need to handle kernel density estimation (KDE) with intricate kernels that are not designed by the user and might even be irregular and asymmetric. To handle this emerging challenge,…

Statistics Theory · Mathematics 2021-06-09 Hau-Tieng Wu , Nan Wu

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…

Probability · Mathematics 2025-12-11 Atef Lechiheb

Supervised learning has recently garnered significant attention in the field of computational physics due to its ability to effectively extract complex patterns for tasks like solving partial differential equations, or predicting material…

Machine Learning · Statistics 2024-03-12 Raphaël Carpintero Perez , Sébastien da Veiga , Josselin Garnier , Brian Staber

Random Feature (RF) models are used as efficient parametric approximations of kernel methods. We investigate, by means of random matrix theory, the connection between Gaussian RF models and Kernel Ridge Regression (KRR). For a Gaussian RF…

Machine Learning · Statistics 2020-09-24 Arthur Jacot , Berfin Şimşek , Francesco Spadaro , Clément Hongler , Franck Gabriel

Identifying dynamical system (DS) is a vital task in science and engineering. Traditional methods require numerous calls to the DS solver, rendering likelihood-based or least-squares inference frameworks impractical. For efficient parameter…

Computation · Statistics 2024-09-19 Ying Zhou , Jinglai Li , Xiang Zhou , Hongqiao Wang
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