Related papers: Locally Adaptive Density Estimation on the Unit Sp…

The problem of existence of adaptive confidence bands for an unknown density $f$ that belongs to a nested scale of H\"{o}lder classes over $\mathbb{R}$ or $[0,1]$ is considered. Whereas honest adaptive inference in this problem is…

A geometry-based density functional theory is presented for mixtures of hard spheres, hard needles and hard platelets; both the needles and the platelets are taken to be of vanishing thickness. Geometrical weight functions that are…

To better understand the dynamics of human settlements, thorough knowledge of the uncertainty in geospatial built-up surface datasets is critical. While frameworks for localized accuracy assessments of categorical gridded data have been…

Given a data set (t_i, y_i), i=1,..., n with the t_i in [0,1] non-parametric regression is concerned with the problem of specifying a suitable function f_n:[0,1] -> R such that the data can be reasonably approximated by the points (t_i,…

We obtain fractal Lipschitz-Killing curvature-direction measures for a large class of self-similar sets F in R^d. Such measures jointly describe the distribution of normal vectors and localize curvature by analogues of the higher order mean…

Density estimation is a crucial component of many machine learning methods, and manifold learning in particular, where geometry is to be constructed from data alone. A significant practical limitation of the current density estimation…

Normalizing Flows (NFs) are universal density estimators based on Neural Networks. However, this universality is limited: the density's support needs to be diffeomorphic to a Euclidean space. In this paper, we propose a novel method to…

We consider the problem of estimating the density $g$ of identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$ and $\sigma \epsilon\_i$ is a noise independent of $X\_i$…

Deep neural networks have shown great achievements in solving complex problems. However, there are fundamental problems that limit their real world applications. Lack of measurable criteria for estimating uncertainty in the network outputs…

This paper reviews and analyses methods used to identify neighbours in 6D space and estimate the corresponding phase-space density. It compares SPH methods to 6D Delaunay tessellation on statical and dynamical realisation of single halo…

We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual…

We aim at estimating in a non-parametric way the density $\pi$ of the stationary distribution of a $d$-dimensional stochastic differential equation $(X_t)_{t \in [0, T]}$, for $d \ge 2$, from the discrete observations of a finite sample…

In the present paper we consider the problem of estimating a three-dimensional function $f$ based on observations from its noisy Laplace convolution. Our study is motivated by the analysis of Dynamic Contrast Enhanced (DCE) imaging data. We…

A scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician. In case of a…

We relate the (anisotropic) variable coefficient local and nonlocal Calder\'on problems by means of the Caffarelli-Silvestre extension. In particular, we prove that (partial) Dirichlet-to-Neumann data for the fractional Calder\'on problem…

Local polynomial density (LPD) estimators are widely used for inference on boundary features of the density function. Contrary to conventional wisdom, we show that kernel choice substantially affects efficiency. Theory, simulations, and…

This paper deals with the problem of density estimation. We aim at building an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Cand\`es and Tao's approach, we propose an $\ell_1$-minimization…

The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…

We consider the problem of estimating the s-th derivative of a density function f by the tilted Kernel estimator introduced in Hall and Doosti (2012). Then we further show this estimator achieves the same convergence rate, in probability,…

Adaptive spatial meshing has proven invaluable for the accurate, efficient computation of solutions of time dependent partial differential equations. In a DA context the use of adaptive spatial meshes addresses several factors that place…