Related papers: Direct Ensemble Estimation of Density Functionals
We formulate the Kohn-Sham density functional theory (KS-DFT) as a statistical theory in which the electron density is deter-mined from an average of correlated stochastic densities in a trace formula. The key idea is that it is sufficient…
How might a smooth probability distribution be estimated, with accurately quantified uncertainty, from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one…
Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators.…
We present an approach based on density-functional theory for the calculation of fundamental gaps of both finite and periodic two-dimensional (2D) electronic systems. The computational cost of our approach is comparable to that of total…
We study the problem of space and time efficient evaluation of a nonparametric estimator that approximates an unknown density. In the regime where consistent estimation is possible, we use a piecewise multivariate polynomial interpolation…
This papers presents a generalization of the Weitzman overlapping coefficient, originally defined for two probability density functions, to a setting involving k independent distributions, denoted by Delta. To estimate this generalized…
We suggest to include the density of electron charge explicitly in the electron potential of density functional theory, rather than implicitly via exchange-correlation functionals. The advantages of the approach are conceptual and…
The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that…
Entropy-type integral functionals of densities are widely used in mathematical statistics, information theory, and computer science. Examples include measures of closeness between distributions (e.g., density power divergence) and…
Nonparametric learning is a fundamental concept in machine learning that aims to capture complex patterns and relationships in data without making strong assumptions about the underlying data distribution. Owing to simplicity and…
The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of ``functional data analysis,'' it has often been assumed that a sample of random functions is observed…
Various studies have confirmed the possibility of identifying the location of a set of small inhomogeneities via a direct sampling method; however, when their permeability differs from that of the background, their location cannot be…
We propose a novel method for density estimation that leverages an estimated score function to debias kernel density estimation (SD-KDE). In our approach, each data point is adjusted by taking a single step along the score function with a…
Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions…
Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of…
Functional Data Analysis represents a field of growing interest in statistics. Despite several studies have been proposed leading to fundamental results, the problem of obtaining valid and efficient prediction sets has not been thoroughly…
Two-sample feature selection is the problem of finding features that describe a difference between two probability distributions, which is a ubiquitous problem in both scientific and engineering studies. However, existing methods have…
Kinetic energy functionals of the electronic density are used to model large systems in the context of density functional theory, without the need to obtain electronic wavefunctions. We discuss the problems associated with the application…
arXiv:2206.10812v1 [stat.ME] proposes a useful algorithm, named generalized Diversity Subsampling (g-DS) algorithm, to select a subsample following some target probability distribution from a finite data set and demonstrates its…
We consider nonparametric estimation of $L_2$, Renyi-$\alpha$ and Tsallis-$\alpha$ divergences between continuous distributions. Our approach is to construct estimators for particular integral functionals of two densities and translate them…