Related papers: Density estimates of 1-avoiding sets via higher or…

We propose a new approach to non-parametric density estimation that is based on regularizing a Sobolev norm of the density. This method is statistically consistent, and makes the inductive bias of the model clear and interpretable. While…

The average distance of the equal hard spheres is introduced to evaluate the density of a given arrangement. The absolute smallest value is two radii because the spheres can not be closer to each other than their diameter. The absolute…

In this paper we present a new bound obtained with the probabilistic method for the solution of the Set Covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic…

It is well known that almost every dilation of a sequence of real numbers, that diverges to $\infty$, is dense modulo~1. This paper studies the exceptional set of points -- those for which the dilation is not dense. Specifically, we…

Projection Pursuit methodology permits to solve the difficult problem of finding an estimate of a density defined on a set of very large dimension. In his seminal article, Huber (see "Projection pursuit", Annals of Statistics, 1985)…

This paper gives a theoretical analysis of high dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis on the poor performances of standard procedures in the case when…

This paper provides the currently best known upper bound on the density of a packing in three-dimensional Euclidean space of two types of spheres whose size ratio is the largest one that allows the insertion of a small sphere in each…

Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model…

The ratio of two probability densities, called a density-ratio, is a vital quantity in machine learning. In particular, a relative density-ratio, which is a bounded extension of the density-ratio, has received much attention due to its…

In this paper, a new sampling scheme of the near field radiated by a planar source is proposed and assessed. More in detail, the paper shows a uniform sampling criterion that allows representing the near field over a plane with a number of…

Estimating a joint Highest Posterior Density credible set for a multivariate posterior density is challenging as dimension gets larger. Credible intervals for univariate marginals are usually presented for ease of computation and…

Identifying anomalies and contamination in datasets is important in a wide variety of settings. In this paper, we describe a new technique for estimating contamination in large, discrete valued datasets. Our approach considers the normal…

Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used to obtain representative centroids of the data manifold for…

In this paper we propose a new method of joint nonparametric estimation of probability density and its support. As is well known, nonparametric kernel density estimator has "boundary bias problem" when the support of the population density…

Line-based density plots are used to reduce visual clutter in line charts with a multitude of individual lines. However, these traditional density plots are often perceived ambiguously, which obstructs the user's identification of…

Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion…

The "visibility" of a planar set $S$ from a point $a$ is defined as the normalized size of the radial projection of $S$ from $a$ to the unit circle centered at $a$. Simon and Solomyak (Real Anal. Exchange 2006/07) proved that unrectifiable…

We derive an analytical expression for a novel large-scale structure observable: the line correlation function. The line correlation function, which is constructed from the three-point correlation function of the phase of the density field,…

Starting from an independent-particle model with a finite and arbitrary set of single-particle energies, we develop an analytical approximation to the many-body level density $\rho_A(E)$ and to particle-hole densities. We use exact…

Density estimation is an interdisciplinary topic at the intersection of statistics, theoretical computer science and machine learning. We review some old and new techniques for bounding the sample complexity of estimating densities of…