Related papers: Self-consistent method for density estimation
Faithful representations of atomic environments and general models for regression can be harnessed to learn electron densities that are close to the ground state. One of the applications of data-derived electron densities is to orbital-free…
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…
The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably…
Synthetic data generation is a promising technique to facilitate the use of sensitive data while mitigating the risk of privacy breaches. However, for synthetic data to be useful in downstream analysis tasks, it needs to be of sufficient…
We propose a frequentist testing procedure that maintains a defined coverage and is optimal in the sense that it gives maximal power to detect deviations from a null hypothesis when the alternative to the null hypothesis is sampled from a…
In a recent Letter, Baer et al. present a stochastic method for Kohn-Sham density functional theory calculations. Their convergence criterion is the self-averaging total energy per electron, which requires a number of statistical samples…
Suppose $X_1,\dots, X_n$ is a random sample from a bounded and decreasing density $f_0$ on $[0,\infty)$. We are interested in estimating such $f_0$, with special interest in $f_0(0)$. This problem is encountered in various statistical…
We consider testing statistical hypotheses about densities of signals in deconvolution models. A new approach to this problem is proposed. We constructed score tests for the deconvolution with the known noise density and efficient score…
Density ratio estimation is a vital tool in both machine learning and statistical community. However, due to the unbounded nature of density ratio, the estimation procedure can be vulnerable to corrupted data points, which often pushes the…
In this article we study the problem of quantifying the uncertainty in an experiment with a technical system. We propose new density estimates which combine observed data of the technical system and simulated data from an (imperfect)…
Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \Psi(t) be a positive continuous function such that \|\Psi f^{\beta}\|_{\infty}<\infty for some 0<\beta<1/2. Under natural…
Divergence estimators based on direct approximation of density-ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
A thesis providing a pedagogical introduction to the problem of achieving self-consistency in density functional theory. Contained is an introduction to the framework of Kohn-Sham density functional theory, leading then to the…
Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…
We estimate on a compact interval densities with isolated irregularities, such as discontinuities or discontinuities in some derivatives. From independent and identically distributed observations we construct a kernel estimator with…
This work considers a problem of estimating a mixing probability density $f$ in the setting of discrete mixture models. The paper consists of three parts. The first part focuses on the construction of an $L_1$ consistent estimator of $f$.…
Histograms are convenient non-parametric density estimators, which continue to be used ubiquitously. Summary quantities estimated from histogram-based probability density models depend on the choice of the number of bins. We introduce a…
We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…
A new framework is presented for evaluating the performance of self-consistent field methods in Kohn-Sham density functional theory. The aims of this work are two-fold. First, we explore the properties of Kohn-Sham density functional theory…