Related papers: Direct Ensemble Estimation of Density Functionals
Kohn-Sham density functional theory is the base of modern computational approaches to electronic structures. Their accuracy vitally relies on the exchange-correlation energy functional, which encapsulates electron-electron interaction…
We propose a novel Bayesian nonparametric method for hierarchical modelling on a set of related density functions, where grouped data in the form of samples from each density function are available. Borrowing strength across the groups is a…
Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed data set. Some of its applications include statistical…
It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation,…
It is a typical standard assumption in the density deconvolution problem that the characteristic function of the measurement error distribution is non-zero on the real line. While this condition is assumed in the majority of existing works…
When nonlinear measures are estimated from sampled temporal signals with finite-length, a radius parameter must be carefully selected to avoid a poor estimation. These measures are generally derived from the correlation integral which…
In this paper, we present a novel way to summarize the structure of large graphs, based on non-parametric estimation of edge density in directed multigraphs. Following coclustering approach, we use a clustering of the vertices, with a…
This paper introduces a novel kernel density estimator (KDE) based on the generalised exponential (GE) distribution, designed specifically for positive continuous data. The proposed GE KDE offers a mathematically tractable form that avoids…
We present a rigorous convergence analysis for cylindrical approximations of nonlinear functionals, functional derivatives, and functional differential equations (FDEs). The purpose of this analysis is twofold: first, we prove that…
A non-parametric k-nearest neighbour based entropy estimator is proposed. It improves on the classical Kozachenko-Leonenko estimator by considering non-uniform probability densities in the region of k-nearest neighbours around each sample…
The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…
We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…
We consider statistical inference for parameters defined by general estimating equations under the covariate shift transfer learning. Different from the commonly used density ratio weighting approach, we undertake a set of formulations to…
Orbital-free density functional theory promises to deliver linear-scaling electronic structure calculations. This requires the knowledge of the non-interacting kinetic-energy density functional (KEDF), which should be accurate and must…
There is a large body of work on convergence rates either in passive or active learning. Here we first outline some of the main results that have been obtained, more specifically in a nonparametric setting under assumptions about the…
Signal-to-noise ratio (SNR) statistics play a central role in many applications. A common situation where SNR is studied is when a continuous time signal is sampled at a fixed frequency with some noise in the background. While estimation…
The density function of the limiting spectral distribution of general sample covariance matrices is usually unknown. We propose to use kernel estimators which are proved to be consistent. A simulation study is also conducted to show the…
Indirect inference estimators (i.e., simulation-based minimum distance estimators) in a parametric model that are based on auxiliary non-parametric maximum likelihood density estimators are shown to be asymptotically normal. If the…
Density functional theory, when applied to systems with $T\neq 0$, is based on the grand canonical extension of the Hohenberg-Kohn-Sham theorem due to Mermin (HKSM theorem). While a straightforward canonical ensemble generalization fails,…
In this paper, Kernel Density Estimation (KDE) as a non-parametric estimation method is used to investigate statistical properties of nuclear spectra. The deviation to regular or chaotic dynamics, is exhibited by closer distances to Poisson…