arXiv Statistics ML

Gaussian Processes with Sample Paths in Reproducing Kernel Banach Spaces

The paper explores the relationship between Gaussian processes and Gaussian random elements within reproducing kernel Banach spaces. It demonstrates that the covariance operator of a weak second‑order Radon probability measure on such a space is uniquely defined by a symmetric positive‑definite function, and in the Gaussian case it identifies which functions correspond to covariance operators via γ‑radonifying operators. Leveraging these findings, the authors extend Driscoll’s theorem to the setting of reproducing kernel Banach spaces.

arXiv Machine Learning

Aug 28

Gaussian Processes and Reproducing Kernel Hilbert Spaces: Connections and Equivalences

The monograph explores the relationships between Gaussian processes and reproducing kernel Hilbert spaces (RKHS), two widely used approaches that rely on positive definite kernels. It examines how these frameworks connect and are equivalent across key topics such as regression, interpolation, numerical integration, distributional discrepancies, statistical dependence, and Gaussian process sample path properties. By establishing a unifying perspective based on the equivalence between the Gaussian Hilbert space and the RKHS, the work aims to bridge methods developed independently by the machine learning, statistics, and numerical analysis communities.

By Motonobu Kanagawa, Philipp Hennig, Dino Sejdinovic, Bharath K. Sriperumbudur

arXiv Statistics ML

6d ago

The kernel mean embedding of a random probability distribution and its principal components

arXiv:2610.33286v1 Announce Type: cross Abstract: Given a random probability distribution $F$, whose realizations are defined on $\mathbb R^d$, and a kernel $k$, our aim is to analyze the prope...

By Amparo Ba\'illo, Mart\'in S\'anchez-Signorini

rag

arXiv Machine Learning

Aug 31

Generalized Splines and Gaussian Processes

arXiv:2608.28446v1 Announce Type: cross Abstract: For finite-dimensional linear inverse problems where the variables are Gaussian, it is well-known that the minimum-mean-square error estimator takes...

By Michael Unser

arXiv Machine Learning

Jun 24

Which Spaces can be Embedded in $L_p$-type Reproducing Kernel Banach Space? A Characterization via Metric Entropy

arXiv:2410. 11116v4 Announce Type: replace-cross Abstract: In this paper, we establish a novel connection between the metric entropy growth and the embeddability of function spaces into reproducing kernel Hilbert/Banach spaces.

By Yiping Lu, Daozhe Lin, Qiang Du

rag

arXiv Machine Learning

Oct 8

Unbounded Characteristic and Universal Kernels

arXiv:2610.09731v1 Announce Type: cross Abstract: Kernel methods are among the most powerful tools in machine learning and statistics, with a large number of successful applications. Their immense su...

By Jose Cribeiro-Ramallo, Florian Kalinke, Zolt\'an Szab\'o

arXiv Statistics ML

Sep 30

A functional central limit theorem for kernel gradient flow and infinitesimal gradient boosting

arXiv:2606.25494v2 Announce Type: replace-cross Abstract: Building on the large-sample analysis of infinitesimal gradient boosting (Dombry and Duchamps, 2024), we study the fluctuations of the proces...

By Cl\'ement Dombry, Jean-Jil Duchamps

agents

Hugging Face Trending Papers

Aug 27

Why not to use the Gaussian kernel

The paper argues against using the Gaussian (squared exponential/RBF) kernel as a default in Gaussian process regression, citing its brittleness. It shows that the kernel leads to unrealistically small conditional variances, causing overconfidence in predictive uncertainty, and that this small variance induces numerical ill‑conditioning, necessitating tricks like nugget terms that alter the model. The authors attribute these issues to the kernel’s analytic, highly smooth nature and suggest that analytic stationary kernels in general should be avoided.

arXiv Machine Learning

Jun 16

Brownian Kernel Ladders

arXiv:2606. 15812v1 Announce Type: new Abstract: Constructing mathematically tractable function spaces that capture hierarchical compositional representations remains a central challenge in statistical learning theory.

By Mahdi Mohammadigohari, Giuseppe Di Fatta, Giuseppe Nicosia, Panos M Pardalos

arXiv Machine Learning

Jul 28

Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD

arXiv:2607. 24235v1 Announce Type: cross Abstract: Over the past 20 years, kernel discrepancies have been leveraged as a highly powerful tool for quantifying the disagreement of distributions, with numerous successful applications in two-sample, goodness-of-fit, and independence testing, among others.

By Jose Cribeiro-Ramallo, Florian Kalinke, Zolt\'an Szab\'o

rag

arXiv Machine Learning

Jul 7

Global universal approximation with Brownian signatures

arXiv:2512. 16396v2 Announce Type: replace-cross Abstract: We establish $L^p$-universal approximation theorems for general path-dependent and non-anticipative functionals on suitable rough path spaces, showing that linear functionals acting on signatures of time-extended rough paths are dense with respect to the $L^p$-distance.

By Mihriban Ceylan, David J. Pr\"omel

Hugging Face Trending Papers

Jun 22

Generalized nonparametric regression in reproducing kernel Hilbert spaces: Consistency and rates of convergence

We develop a comprehensive theory for regularized M-estimation in reproducing kernel Hilbert spaces. Under mild conditions on the loss we establish existence and measurability of the estimator, covering a wide range of convex and non-convex losses, including bounded robust losses.

safety

arXiv Machine Learning

Jul 15

Spectral Diffusion Processes

arXiv:2209. 14125v3 Announce Type: replace-cross Abstract: Diffusion models have proven to be a flexible and effective framework for modelling probability distributions on finite-dimensional spaces.

By Angus Phillips, Thomas Seror, Michael Hutchinson, Valentin De Bortoli, Arnaud Doucet, Emile Mathieu

diffusion multimodal

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