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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

Density ratio estimation serves as an important technique in the unsupervised machine learning toolbox. However, such ratios are difficult to estimate for complex, high-dimensional data, particularly when the densities of interest are…

Machine Learning · Computer Science 2021-07-07 Kristy Choi , Madeline Liao , Stefano Ermon

A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear…

Statistics Theory · Mathematics 2023-04-20 Yoshihito Kazashi , Fabio Nobile

We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…

Statistics Theory · Mathematics 2024-04-19 Raphaël Maillet , Grégoire Szymanski

Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…

Methodology · Statistics 2019-10-08 Vitaliy Oryshchenko , Richard J. Smith

This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The…

Methodology · Statistics 2022-03-04 Kiheiji Nishida

Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density.…

Statistics Theory · Mathematics 2019-01-03 Maciej Skorski

In the context of kernel density estimation, we give a characterization of the kernels for which the parametric mean integrated squared error rate $n^{-1}$ may be obtained, where $n$ is the sample size. Also, for the cases where this rate…

Statistics Theory · Mathematics 2011-11-22 J. E. Chacón , J. Montanero , A. G. Nogales

One key issue in several astrophysical problems is the evaluation of the density probability function underlying an observational discrete data set. We here review two non-parametric density estimators which recently appeared in the…

Astrophysics · Physics 2009-10-30 Dario Fadda , Eric Slezak , Albert Bijaoui

A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…

Statistics Theory · Mathematics 2015-10-02 Piero Barone

This study proposes multivariate kernel density estimation by stagewise minimization algorithm based on $U$-divergence and a simple dictionary. The dictionary consists of an appropriate scalar bandwidth matrix and a part of the original…

Machine Learning · Statistics 2021-08-11 Kiheiji Nishida , Kanta Naito

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

The standard definition of pedestrian density produces scattered values, hence, many approaches have been developed to improve the features of the estimated density. This paper provides a review of generally applied methods and presents a…

Physics and Society · Physics 2023-07-18 Jana Vacková , Marek Bukáček

We derive concentration inequalities for the supremum norm of the difference between a kernel density estimator (KDE) and its point-wise expectation that hold uniformly over the selection of the bandwidth and under weaker conditions on the…

Statistics Theory · Mathematics 2020-01-01 Jisu Kim , Jaehyeok Shin , Alessandro Rinaldo , Larry Wasserman

This paper deals with the kernel density estimator based on the so-called sinc (or Fourier integral) kernel $K(x)=(\pi x)^{-1}\sin x$. We study in detail both asymptotic and finite sample properties of this estimator. It is shown that,…

Statistics Theory · Mathematics 2026-05-11 Ingrid Kristine Glad , Nils Lid Hjort , Nikolai G. Ushakov

We are studying the problem of estimating density in a wide range of metric spaces, including the Euclidean space, the sphere, the ball, and various Riemannian manifolds. Our framework involves a metric space with a doubling measure and a…

Statistics Theory · Mathematics 2023-04-04 Galatia Cleanthous , Athanasios G. Georgiadis , Philip A. White

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 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

When analyzing modern machine learning algorithms, we may need to handle kernel density estimation (KDE) with intricate kernels that are not designed by the user and might even be irregular and asymmetric. To handle this emerging challenge,…

Statistics Theory · Mathematics 2021-06-09 Hau-Tieng Wu , Nan Wu

Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical…

Machine Learning · Statistics 2025-10-02 Dehao Dai , Jianqing Fan , Yihong Gu , Debarghya Mukherjee