Hugging Face Trending Papers

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.

arXiv Machine Learning

Aug 7

Verifiable Regularity Criterion for Conditional Expectation Operators and Conditional Mean Embeddings with Applications to Nonparametric Regression, Bayesian Inverse Problems, and Koopman Operators

arXiv:2608. 06155v1 Announce Type: cross Abstract: Conditional expectation operators (CEOs) and their associated conditional mean embeddings (CMEs) play a central role across applied mathematics and machine learning, appearing in nonparametric regression, Bayesian inverse problems, and Koopman operator theory.

By Maximiliano Hertel, Ilja Klebanov, Manuel Schaller, Karl Worthmann

rag

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 9

Statistical inverse learning and $\ell^1$-regularization

arXiv:2607. 07468v1 Announce Type: cross Abstract: We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning.

By Abhishake Rastogi, Tatiana A. Bubba, Tapio Helin, Luca Ratti

efficiency

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

Jun 16

Representation Costs in Data Science: Foundations and the Quasi-Banach Spaces of Deep Neural Networks

arXiv:2606. 14954v1 Announce Type: cross Abstract: We develop a general framework for analyzing representation costs of parametric data-fitting methods through their parameter-space regularizers.

By Greg Ongie, Rahul Parhi

safety

arXiv Machine Learning

Jul 10

Optimal uncertainty bounds for multivariate kernel regression under bounded noise: A Gaussian process-based dual function

arXiv:2603. 16481v3 Announce Type: replace Abstract: Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data, and thus, a key enabler for safe learning-based control.

By Amon Lahr, Anna Scampicchio, Johannes K\"ohler, Melanie N. Zeilinger

arXiv Machine Learning

6d ago

A Variational Analysis of Kernel Learning with Learnable Linear Transformations

arXiv:2502. 11665v3 Announce Type: replace-cross Abstract: The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel Hilbert space, such as a Sobolev space.

By Yang Li, Feng Ruan

arXiv Machine Learning

Jul 10

Statistical inverse learning problems with random observations

arXiv:2312. 15341v1 Announce Type: cross Abstract: We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems.

By Abhishake Rastogi, Tapio Helin, Nicole M\"ucke

arXiv Machine Learning

Jul 13

Near-optimal Delta-convex Estimation of Lipschitz Functions

arXiv:2511. 15615v2 Announce Type: replace-cross Abstract: This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate.

By G\'abor Bal\'azs

arXiv Machine Learning

Jun 17

Generalization Guarantees for Multi-Input Neural Operator Learning in Sobolev Spaces

arXiv:2606. 17419v1 Announce Type: new Abstract: We develop approximation and generalization error estimates for multi-input neural operators, with the output error measured in Sobolev norms.

By Yahong Yang, Zecheng Zhang, Wei Zhu, Wenjing Liao, Hao Liu

arXiv Machine Learning

6d ago

Kernel Methods for Learning Operators with Multiple Inputs and Outputs

arXiv:2608. 11831v1 Announce Type: new Abstract: Learning mappings between infinite-dimensional objects is a central challenge in scientific machine learning.

By Adrien Weihs, Chunyang Liao, Jingmin Sun, Hayden Schaeffer

benchmarks

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

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