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We propose a generative model that achieves minimax-optimal convergence rates for estimating probability distributions supported on unknown low-dimensional manifolds. Building on Fefferman's solution to the geometric Whitney problem, our…

Statistics Theory · Mathematics 2025-06-25 Arthur Stéphanovitch

We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d.~data from the mixture model, using ideas from shape…

Methodology · Statistics 2015-11-10 Rohit Kumar Patra , Bodhisattva Sen

A completely nonparametric method for the estimation of mixture cure models is proposed. A nonparametric estimator of the incidence is extensively studied and a nonparametric estimator of the latency is presented. These estimators, which…

Methodology · Statistics 2024-01-31 Ana López-Cheda , Ricardo Cao , M. Amalia Jácome , Ingrid Van Keilegom

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

Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…

Machine Learning · Computer Science 2012-06-22 Samuel Gershman , Matt Hoffman , David Blei

Reconstruction of sets from a random sample of points intimately related to them is the goal of set estimation theory. Within this context, a particular problem is the one related with the reconstruction of density level sets and…

Methodology · Statistics 2020-11-06 Paula Saavedra-Nieves , Rosa María Crujeiras

We consider the problem of Bayesian density estimation on the positive semiline for possibly unbounded densities. We propose a hierarchical Bayesian estimator based on the gamma mixture prior which can be viewed as a location mixture. We…

Statistics Theory · Mathematics 2020-02-25 Natalia Bochkina , Judith Rousseau

Given a sample of independent and identically distributed random variables, a novel nonparametric maximum entropy method is presented to estimate the underlying continuous univariate probability density function (pdf). Estimates are found…

Probability · Mathematics 2016-06-30 Jenny Farmer , Donald J. Jacobs

In this paper, we consider the alleviation of the boundary problem when the probability density function has bounded support. We apply Robbins-Monro's algorithm and Bernstein polynomials to construct a recursive density estimator. We study…

Statistics Theory · Mathematics 2019-04-16 Yousri SLAOUI , Asma JMAEI

When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…

Machine Learning · Computer Science 2013-02-21 George H. John , Pat Langley

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

This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…

Statistics Theory · Mathematics 2010-08-18 Jimmy Olsson , Jonas Ströjby

Density estimation plays a fundamental role in many areas of statistics and machine learning. Parametric, nonparametric and semiparametric density estimation methods have been proposed in the literature. Semiparametric density models are…

Statistics Theory · Mathematics 2019-01-11 Jian Shi , Jiahui Yu , Anna Liu , Yuedong Wang

This paper presents a comprehensive study of nonparametric estimation techniques on the circle using Fej\'er polynomials, which are analogues of Bernstein polynomials for periodic functions. Building upon Fej\'er's uniform approximation…

Methodology · Statistics 2025-01-16 Bernhard Klar , Bojana Milošević , Marko Obradović

We consider nonparametric measurement error density deconvolution subject to heteroscedastic measurement errors as well as symmetry about zero and shape constraints, in particular unimodality. The problem is motivated by applications where…

Methodology · Statistics 2020-02-19 Ya Su , Anirban Bhattacharya , Yan Zhang , Nilanjan Chatterjee , Raymond J. Carroll

Mixture Density Networks (MDNs) can be used to generate probability density functions of model parameters $\boldsymbol{\theta}$ given a set of observables $\mathbf{x}$. In some applications, training data are available only for discrete…

Data Analysis, Statistics and Probability · Physics 2021-08-18 Charles Burton , Spencer Stubbs , Peter Onyisi

To consider model uncertainty in global Fr\'{e}chet regression and improve density response prediction, we propose a frequentist model averaging method. The weights are chosen by minimizing a cross-validation criterion based on Wasserstein…

Methodology · Statistics 2023-09-06 Xingyu Yan , Xinyu Zhang , Peng Zhao

Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used…

Machine Learning · Statistics 2020-07-17 Avinava Dubey , Michael Minyi Zhang , Eric P. Xing , Sinead A. Williamson

This paper shows that the Poisson multi-Bernoulli mixture (PMBM) density is a multi-target conjugate prior for general target-generated measurement distributions and arbitrary clutter distributions. That is, for this multi-target…

Applications · Statistics 2023-05-25 Ángel F. García-Fernández , Yuxuan Xia , Lennart Svensson

The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…

Methodology · Statistics 2021-03-04 Vincenzo Gioia , Euloge Clovis Kenne Pagui