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Kernel normalization methods have been employed to improve robustness of optimization methods to reparametrization of convolution kernels, covariate shift, and to accelerate training of Convolutional Neural Networks (CNNs). However, our…

Computer Vision and Pattern Recognition · Computer Science 2016-10-25 Mete Ozay , Takayuki Okatani

Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel…

Statistics Theory · Mathematics 2024-02-05 Jianfa Lai , Zhifan Li , Dongming Huang , Qian Lin

We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…

Statistics Theory · Mathematics 2017-06-13 Marco Singer , Tatyana Krivobokova , Axel Munk

For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks,…

Machine Learning · Computer Science 2025-01-07 Hrushikesh Mhaskar

Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect…

Machine Learning · Computer Science 2024-01-17 Xiaotong Liu , Jinxin Wang , Di Wang , Shao-Bo Lin

In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region which is defined by a set of linear inequalities involving…

Statistics Theory · Mathematics 2007-11-06 P. L. Davies , A. Kovac , M. Meise

Random forest regression is a powerful non-parametric method that adapts to local data characteristics through data-driven partitioning, making it effective across diverse application domains. However, the piecewise constant nature of…

Machine Learning · Computer Science 2026-05-19 Ziyi Liu , Phuc Luong , Mario Boley , Daniel F. Schmidt

We propose a novel class of kernels to alleviate the high computational cost of large-scale nonparametric learning with kernel methods. The proposed kernel is defined based on a hierarchical partitioning of the underlying data domain, where…

Machine Learning · Computer Science 2017-08-15 Jie Chen , Haim Avron , Vikas Sindhwani

As modern machine learning models continue to advance the computational frontier, it has become increasingly important to develop precise estimates for expected performance improvements under different model and data scaling regimes.…

Machine Learning · Computer Science 2023-06-13 Lechao Xiao , Hong Hu , Theodor Misiakiewicz , Yue M. Lu , Jeffrey Pennington

Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…

Statistics Theory · Mathematics 2024-12-12 Naveen Gupta , S. Sivananthan , Bharath K. Sriperumbudur

We apply a fast kernel method for mask-based single-channel speech enhancement. Specifically, our method solves a kernel regression problem associated to a non-smooth kernel function (exponential power kernel) with a highly efficient…

Machine Learning · Computer Science 2018-11-07 Like Hui , Siyuan Ma , Mikhail Belkin

We study kernel-based estimation of nonparametric time-varying parameters (TVPs) in linear models. Our contributions are threefold. First, we establish consistency and asymptotic normality of the kernel-based estimator for a broad class of…

Econometrics · Economics 2026-01-26 Mikihito Nishi

In this work we investigate the variation of the online kernelized ridge regression algorithm in the setting of $d-$dimensional adversarial nonparametric regression. We derive the regret upper bounds on the classes of Sobolev spaces…

Statistics Theory · Mathematics 2021-07-14 Oleksandr Zadorozhnyi , Pierre Gaillard , Sebastien Gerschinovitz , Alessandro Rudi

Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…

Machine Learning · Statistics 2020-07-01 Yuhao Zhou , Jiaxin Shi , Jun Zhu

We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…

Statistics Theory · Mathematics 2018-03-14 Joshua Lee Mike , Vasileios Maroulas

We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing…

Numerical Analysis · Mathematics 2025-12-24 Oleg Davydov

Over-parameterized models like deep nets and random forests have become very popular in machine learning. However, the natural goals of continuity and differentiability, common in regression models, are now often ignored in modern…

Machine Learning · Computer Science 2023-10-16 Mingxuan Han , Varun Shankar , Jeff M Phillips , Chenglong Ye

Statistical analysis is increasingly confronted with complex data from metric spaces. Petersen and M\"uller (2019) established a general paradigm of Fr\'echet regression with complex metric space valued responses and Euclidean predictors.…

Machine Learning · Statistics 2025-02-10 Rui Qiu , Zhou Yu , Ruoqing Zhu

This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…

Numerical Analysis · Mathematics 2020-08-12 Rishi Advani , Madison Crim , Sean O'Hagan

The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…

Machine Learning · Computer Science 2022-09-13 Paul Scharnhorst , Emilio T. Maddalena , Yuning Jiang , Colin N. Jones