Related papers: Resample-smoothing of Voronoi intensity estimators

Given two sets of training samples, general method is to estimate the density function and classify the test sample according to higher values of estimated densities. Natural way to estimate the density should be histogram tending to…

The Voronoi Density Estimator (VDE) is an established density estimation technique that adapts to the local geometry of data. However, its applicability has been so far limited to problems in two and three dimensions. This is because…

We consider the nonparametric estimation of the intensity function of a Poisson point process in a circular model from indirect observations $N_1,\ldots,N_n$. These observations emerge from hidden point process realizations with the target…

In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques…

For a group of pedestrians without any spatial boundaries, the methods of density estimation is a wide area of research. Besides, there is a specific difficulty when the density along one given pedestrian trajectory is needed in order to…

A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias…

We introduce a new variational estimator for the intensity function of an inhomogeneous spatial point process with points in the $d$-dimensional Euclidean space and observed within a bounded region. The variational estimator applies in a…

Intensity estimation for Poisson processes is a classical problem and has been extensively studied over the past few decades. Practical observations, however, often contain compositional noise, i.e. a nonlinear shift along the time axis,…

Information retrieval (IR) systems traditionally aim to maximize metrics built on rankings, such as precision or NDCG. However, the non-differentiability of the ranking operation prevents direct optimization of such metrics in…

We introduce two new methods to obtain reliable velocity field statistics from N-body simulations, or indeed from any general density and velocity fluctuation field sampled by discrete points. These methods, the {\it Voronoi tessellation…

For pedestrians moving without spatial constraints, extensive research has been devoted to develop methods of density estimation. In this paper we present a new approach based on Voronoi cells, offering a means to estimate density for…

Expected values weighted by the inverse of a multivariate density or, equivalently, Lebesgue integrals of regression functions with multivariate regressors occur in various areas of applications, including estimating average treatment…

I present a regression algorithm that provides a continuous, piecewise-smooth function approximating scattered data. It is based on composing and blending linear functions over Voronoi cells, and it scales to high dimensions. The algorithm…

Since state-of-the-art uncertainty estimation methods are often computationally demanding, we investigate whether incorporating prior information can improve uncertainty estimates in conventional deep neural networks. Our focus is on…

We study the problem of decomposing a volume bounded by a smooth surface into a collection of Voronoi cells. Unlike the dual problem of conforming Delaunay meshing, a principled solution to this problem for generic smooth surfaces remained…

The availability of large spatial data geocoded at accurate locations has fueled a growing interest in spatial modeling and analysis of point processes. The proposed research is motivated by the intensity estimation problem for large…

We introduce a non-parametric density estimator deemed Radial Voronoi Density Estimator (RVDE). RVDE is grounded in the geometry of Voronoi tessellations and as such benefits from local geometric adaptiveness and broad convergence…

Large samples have been generated routinely from various sources. Classic statistical models, such as smoothing spline ANOVA models, are not well equipped to analyze such large samples due to expensive computational costs. In particular,…

Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…

Sobolev quantities (norms, inner products, and distances) of probability density functions are important in the theory of nonparametric statistics, but have rarely been used in practice, partly due to a lack of practical estimators. They…