Related papers: Numerical estimation of densities
We consider the problem of reconstructing the intrinsic geometry of a manifold from noisy pairwise distance observations. Specifically, let $M$ denote a diameter 1 d-dimensional manifold and $\mu$ a probability measure on $M$ that is…
The size of datasets has been increasing rapidly both in terms of number of variables and number of events. As a result, the empty space phenomenon and the curse of dimensionality complicate the extraction of useful information. But, in…
Sampling-based methods, e.g., Deep Ensembles and Bayesian Neural Nets have become promising approaches to improve the quality of uncertainty estimation and robust generalization. However, they suffer from a large model size and high latency…
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…
Voronoi intensity estimators, which are non-parametric estimators for intensity functions of point processes, are both parameter-free and adaptive; the intensity estimate at a given location is given by the reciprocal size of the…
Dense crowd counting aims to predict thousands of human instances from an image, by calculating integrals of a density map over image pixels. Existing approaches mainly suffer from the extreme density variances. Such density pattern shift…
This article investigates reconstructing the internal mass density of a numerical asteroid model using the gradient of a simulated gravity field as synthetic measurement data. Our goal is to advance the mathematical inversion methodology…
Numerical precision in large-scale scientific computations has become an emerging topic due to recent developments in computer hardware. Lower floating point precision offers the potential for significant performance improvements, but the…
The density deconvolution problem involves recovering a target density g from a sample that has been corrupted by noise. From the perspective of Le Cam's local asymptotic normality theory, we show that non-parametric density deconvolution…
Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…
Density deconvolution deals with the estimation of the probability density function $f$ of a random signal from $n\geq1$ data observed with independent and known additive random noise. This is a classical problem in statistics, for which…
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for…
Clustering is a cornerstone of modern data analysis. Detecting clusters in exploratory data analyses (EDA) requires algorithms that make few assumptions about the data. Density-based clustering algorithms are particularly well-suited for…
We introduce a new cell-centered finite volume discretization for elasticity with weakly enforced symmetry of the stress tensor. The method is motivated by the need for robust discretization methods for deformation and flow in porous media,…
Downsampling and feature extraction are essential procedures for 3D point cloud understanding. Existing methods are limited by the inconsistent point densities of different parts in the point cloud. In this work, we analyze the limitation…
This work investigates a fully discrete mixed finite element method for the stochastic Boussinesq system driven by multiplicative noise. The spatial discretization is performed using a standard mixed finite element method, while the…
In this paper we refine the procedure proposed by Lin et al. (2015) to estimate the density at a given quantile based on a resampling method. The approach consists on generating multiple samples of the zero-mean Gaussian variable from which…
Context. Weak lensing and clustering statistics beyond two-point functions can capture non-Gaussian information about the matter density field, thereby improving the constraints on cosmological parameters relative to the mainstream methods…
Most existing image denoising approaches assumed the noise to be homogeneous white Gaussian distributed with known intensity. However, in real noisy images, the noise models are usually unknown beforehand and can be much more complex. This…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…