Related papers: The Effective Number of Parameters in Kernel Densi…
A direct orbital optimization method is presented for density functional calculations of excited electronic states using either a real space grid or a plane wave basis set. The method is variational, provides atomic forces in the excited…
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…
Beyond their impressive sampling capabilities, score-based diffusion models offer a powerful analysis tool in the form of unbiased density estimation of a query sample under the training data distribution. In this work, we investigate the…
Orbital-free density functional theory (OF-DFT) constitutes a computationally highly effective tool for modeling electronic structures of systems ranging from room-temperature materials to warm dense matter. Its accuracy critically depends…
An objective Bayesian approach to estimate the number of degrees of freedom $(\nu)$ for the multivariate $t$ distribution and for the $t$-copula, when the parameter is considered discrete, is proposed. Inference on this parameter has been…
The finite basis optimized effective potential (OEP) method within density functional theory is examined as an ill-posed problem. It is shown that the generation of nonphysical potentials is a controllable manifestation of the use of…
Density ratio estimation (DRE) is a useful tool for quantifying discrepancies between probability distributions, but existing approaches often involve a trade-off between estimation quality and computational efficiency. Classical direct DRE…
With the sharp rise in software dependability and failure cost, high quality has been in great demand. However, guaranteeing high quality in software systems which have grown in size and complexity coupled with the constraints imposed on…
When analyzing modern machine learning algorithms, we may need to handle kernel density estimation (KDE) with intricate kernels that are not designed by the user and might even be irregular and asymmetric. To handle this emerging challenge,…
Recent astronomical observations, nuclear-reaction experiments, and microscopic calculations have placed new constraints on the nuclear equation of state (EoS) and revealed that most nuclear structure models fail to satisfy those…
We introduce a new nonparametric density estimator inspired by Markov Chains, and generalizing the well-known Kernel Density Estimator (KDE). Our estimator presents several benefits with respect to the usual ones and can be used…
In the density functional (DF) theory of Kohn and Sham, the kinetic energy of the ground state of a system of noninteracting electrons in a general external field is calculated using a set of orbitals. Orbital free methods attempt to…
We study efficient mechanisms for differentially private kernel density estimation (DP-KDE). Prior work for the Gaussian kernel described algorithms that run in time exponential in the number of dimensions $d$. This paper breaks the…
Kernel density estimation (KDE) has become a popular method for visual analysis in various fields, such as financial risk forecasting, crime clustering, and traffic monitoring. KDE can identify high-density areas from discrete datasets.…
We provide an empirical process theory for locally stationary processes over nonsmooth function classes. An important novelty over other approaches is the use of the flexible functional dependence measure to quantify dependence. A…
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…
In this paper, we construct a moment inequality for mixing dependent random variables, it is of independent interest. As applications, the consistency of the kernel density estimation is investigated. Several limit theorems are established:…
Nuclear Density Functional Theory (DFT) plays a prominent role in the understanding of nuclear structure, being the approach with the widest range of applications. Hohenberg and Kohn theorems warrant the existence of a nuclear Energy…
In this paper, we introduce a robust nonparametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE). This estimator is shown to achieve robustness to any kind of anomalous…
The explicit density (rho) dependence in the coupling coefficients of the non-relativistic nuclear energy-density functional (EDF) encodes effects of three-nucleon forces and dynamical correlations. The necessity for a coupling coefficient…