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This paper considers different facets of the interplay between reproducing kernel Hilbert spaces (RKHS) and stable analysis/synthesis processes: First, we analyze the structure of the reproducing kernel of a RKHS using frames and…

Functional Analysis · Mathematics 2019-04-02 Michael Speckbacher , Peter Balazs

This paper investigates a novel algorithmic approach to data representation based on kernel methods. Assuming that the observations lie in a Hilbert space X, the introduced Kernel Autoencoder (KAE) is the composition of mappings from…

Machine Learning · Statistics 2020-12-03 Pierre Laforgue , Stephan Clémençon , Florence d'Alché-Buc

We propose to estimate a metamodel and the sensitivity indices of a complex model m in the Gaussian regression framework. Our approach combines methods for sensitivity analysis of complex models and statistical tools for sparse…

Statistics Theory · Mathematics 2019-11-19 Sylvie Huet , Marie-Luce Taupin

In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued…

Operator Algebras · Mathematics 2024-10-14 Palle E. T. Jorgensen , James Tian

This paper establishes a kernel-based framework for reconstructing data on manifolds, tailored to fit the dynamic-(d)MRI-data recovery problem. The proposed methodology exploits simple tangent-space geometries of manifolds in reproducing…

Machine Learning · Computer Science 2020-02-28 Gaurav N. Shetty , Konstantinos Slavakis , Ukash Nakarmi , Gesualdo Scutari , Leslie Ying

In this work, we investigate the generalization properties of random feature methods. Our analysis extends prior results for Tikhonov regularization to a broad class of spectral regularization techniques and further generalizes the setting…

Machine Learning · Statistics 2026-03-03 Mike Nguyen , Nicole Mücke

Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…

Optimization and Control · Mathematics 2025-01-27 Vladimir Norkin , Alois Pichler

We show that polynomials do not belong to the reproducing kernel Hilbert space of infinitely differentiable translation-invariant kernels whose spectral measures have moments corresponding to a determinate moment problem. Our proof is based…

Statistics Theory · Mathematics 2021-08-13 Holger Dette , Anatoly Zhigljavsky

There are two things to be considered when we evaluate predictive models. One is prediction accuracy,and the other is interpretability. Over the recent decades, many prediction models of high performance, such as ensemble-based models and…

Machine Learning · Statistics 2024-08-05 Yongchan Choi , Seokhun Park , Chanmoo Park , Dongha Kim , Yongdai Kim

In this article, we develop a kernel-based framework for constructing dynamic, pathdependent trading strategies under a mean-variance optimisation criterion. Building on the theoretical results of (Muca Cirone and Salvi, 2025), we…

Trading and Market Microstructure · Quantitative Finance 2025-07-16 Owen Futter , Nicola Muca Cirone , Blanka Horvath

This work provides theoretical foundations for kernel methods in the hyperspherical context. Specifically, we characterise the native spaces (reproducing kernel Hilbert spaces) and the Sobolev spaces associated with kernels defined over…

Machine Learning · Statistics 2022-11-18 Simon Hubbert , Emilio Porcu , Chris. J. Oates , Mark Girolami

In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…

Statistics Theory · Mathematics 2021-11-01 Keli Guo , Jun Fan , Lixing Zhu

This paper proposes a new nonlinear approach for additive functional regression with functional response based on kernel methods along with some slight reformulation and implementation of the linear regression and the spectral additive…

The reproducing kernel Hilbert space (RKHS) embedding of distributions offers a general and flexible framework for testing problems in arbitrary domains and has attracted considerable amount of attention in recent years. To gain insights…

Machine Learning · Statistics 2017-09-26 Krishnakumar Balasubramanian , Tong Li , Ming Yuan

Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions. Operators acting on…

Functional Analysis · Mathematics 2021-04-06 Mattes Mollenhauer , Ingmar Schuster , Stefan Klus , Christof Schütte

Compositional data, such as human gut microbiomes, consist of non-negative variables whose only the relative values to other variables are available. Analyzing compositional data such as human gut microbiomes needs a careful treatment of…

Machine Learning · Statistics 2022-05-04 Binglin Li , Jeongyoun Ahn

We propose a new decentralized robust kernel-based learning algorithm within the framework of reproducing kernel Hilbert spaces (RKHSs) by utilizing a networked system that can be represented as a connected graph. The robust loss function…

Machine Learning · Computer Science 2025-08-18 Zhan Yu , Zhongjie Shi , Ding-Xuan Zhou

The main purpose of our paper is a new approach to design of algorithms of Kaczmarz type in the framework of operators in Hilbert space. Our applications include a diverse list of optimization problems, new Karhunen-Lo\`eve transforms, and…

Functional Analysis · Mathematics 2021-04-27 Palle E. T. Jorgensen , Myung-Sin Song , James Tian

We study distributed learning with the least squares regularization scheme in a reproducing kernel Hilbert space (RKHS). By a divide-and-conquer approach, the algorithm partitions a data set into disjoint data subsets, applies the least…

Machine Learning · Computer Science 2017-03-14 Shao-Bo Lin , Xin Guo , Ding-Xuan Zhou

Complex models are often used to understand interactions and drivers of human-induced and/or natural phenomena. It is worth identifying the input variables that drive the model output(s) in a given domain and/or govern specific model…

Methodology · Statistics 2023-11-07 Matieyendou Lamboni