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This paper presents an intuitive application of multivariate kernel density estimation (KDE) for data correction. The method utilizes the expected value of the conditional probability density function (PDF) and a credible interval to…

Applications · Statistics 2025-09-19 Hai Bui , Mostafa Bakhoday-Paskyabi

Estimating the ratio of two probability densities from finitely many samples, is a central task in machine learning and statistics. In this work, we show that a large class of kernel methods for density ratio estimation suffers from error…

Machine Learning · Computer Science 2024-06-04 Lukas Gruber , Markus Holzleitner , Johannes Lehner , Sepp Hochreiter , Werner Zellinger

A Wishart kernel density estimator (KDE) is introduced for density estimation in the cone of positive definite matrices. The estimator is boundary-aware and mitigates the boundary bias suffered by conventional KDEs, while remaining simple…

Methodology · Statistics 2025-12-10 Léo R. Belzile , Christian Genest , Frédéric Ouimet , Donald Richards

In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…

Statistics Theory · Mathematics 2008-12-18 Aurore Delaigle , Peter Hall , Alexander Meister

In this paper, we consider the nonparametric estimation of the multivariate probability density function and its partial derivative with a support on $[0,\infty)$. To this end we use the class of kernel estimators with asymmetric gamma…

Probability · Mathematics 2017-12-27 L. A. Markovich

Despite the ubiquity of kernel-based clustering, surprisingly few statistical guarantees exist beyond settings that consider strong structural assumptions on the data generation process. In this work, we take a step towards bridging this…

Machine Learning · Computer Science 2021-10-19 Leena Chennuru Vankadara , Sebastian Bordt , Ulrike von Luxburg , Debarghya Ghoshdastidar

We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…

Machine Learning · Statistics 2021-11-02 Ingo Steinwart , Bharath K. Sriperumbudur , Philipp Thomann

We investigate the issue of bandwidth estimation in a nonparametric functional regression model with function-valued, continuous real-valued and discrete-valued regressors under the framework of unknown error density. Extending from the…

Methodology · Statistics 2016-06-20 Han Lin Shang

We review recent advances in modal regression studies using kernel density estimation. Modal regression is an alternative approach for investigating relationship between a response variable and its covariates. Specifically, modal regression…

Methodology · Statistics 2017-12-08 Yen-Chi Chen

Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most…

Machine Learning · Computer Science 2022-08-08 Joseph A. Gallego , Juan F. Osorio , Fabio A. González

We determine the expected error by smoothing the data locally. Then we optimize the shape of the kernel smoother to minimize the error. Because the optimal estimator depends on the unknown function, our scheme automatically adjusts to the…

Methodology · Statistics 2019-11-19 Kurt S. Riedel , A. Sidorenko

Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in problems involving sparse or low-rank data. We show that…

Machine Learning · Computer Science 2023-10-02 Jason M. Altschuler , Pablo A. Parrilo

The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…

Statistics Theory · Mathematics 2023-02-07 Rafail Kartsioukas , Stilian Stoev , Tailen Hsing

The rate of normal approximation for the integral norm of kernel density estimators is investigated in the case of densities with power-type singularities. The quantities from the formulations of published results by the author are…

Probability · Mathematics 2018-05-22 Andrei Yu. Zaitsev

A density estimation method in a Bayesian nonparametric framework is presented when recorded data are not coming directly from the distribution of interest, but from a length biased version. From a Bayesian perspective, efforts to…

Statistics Theory · Mathematics 2015-10-23 Spyridon J. Hatjispyros , Theodoros Nicoleris , Stephen G. Walker

We describe a method for fitting distributions to data which only requires knowledge of the parametric form of either the signal or the background but not both. The unknown distribution is fit using a non-parametric kernel density…

Data Analysis, Statistics and Probability · Physics 2015-06-03 Wolfgang A. Rolke , Angel M. López

An accurate sea clutter distribution is crucial for decision region determination when detecting sea-surface floating targets. However, traditional parametric models possibly have a considerable gap to the realistic distribution of sea…

Applications · Statistics 2018-09-10 Hongkuan Zhou , Yuzhou Li , Tao Jiang

Approximate Bayesian computation (ABC) is a likelihood-free approach for Bayesian inferences based on a rejection algorithm method that applies a tolerance of dissimilarity between summary statistics from observed and simulated data.…

Populations and Evolution · Quantitative Biology 2013-09-26 Shigeki Nakagome , Kenji Fukumizu , Shuhei Mano

Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting…

Machine Learning · Statistics 2019-12-20 Diego Granziol , Robin Ru , Stefan Zohren , Xiaowen Dong , Michael Osborne , Stephen Roberts

We introduce an alternative method for the calculation of sky maps from data taken with gamma-ray telescopes. In contrast to the established method of smoothing the 2D histogram of reconstructed event directions with a static kernel, we…

High Energy Astrophysical Phenomena · Physics 2024-01-30 M. Holler , T. Mitterdorfer , S. Panny