Related papers: The Effective Number of Parameters in Kernel Densi…
Given a sample $\{X_i\}_{i=1}^n$ from $f_X$, we construct kernel density estimators for $f_Y$, the convolution of $f_X$ with a known error density $f_{\epsilon}$. This problem is known as density estimation with Berkson error and has…
We develop a method to evaluate the generalized degrees of freedom (GDF), which is a key quantity of a model selection criterion, for linear regression with sparse regularization. Using the replica method, GDF is expressed by the variables…
Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic…
Despite a large number of nonlocal kinetic energy density functionals (KEDFs) available for large-scale calculations, most of those nonlocal KEDFs designed for the extended systems cannot be directly applied to isolated systems. In this…
We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual…
Extended Lagrangian Born-Oppenheimer molecular dynamics [{\em Phys.\ Rev.\ Lett.\ } {\bf 2008}, {\em 100}, 123004] is presented for Hartree-Fock theory, where the extended electronic degrees of freedom are represented by a density matrix,…
Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density.…
Within ``orbital-free'' density functional theory, it is essential to develop general kinetic energy density (KED), denoted as $t(\mathbf{r})$. This is usually done by empirical corrections and enhancements, gradient expansions, machine…
We focus on the nonparametric density estimation problem with directional data. We propose a new rule for bandwidth selection for kernel density estimation. Our procedure is automatic, fully data-driven and adaptive to the smoothness degree…
In the framework of an equation of state (EoS) constructed from a momentum and density-dependent finite-range two-body effective interaction, the quantitative magnitudes of the different symmetry elements of infinite nuclear matter are…
Orbital-Free Density Functional Theory (OF-DFT) promises to describe the electronic structure of very large quantum systems, being its computational cost linear with the system size. However, the OF-DFT accuracy strongly depends on the…
Density functional theory has been an essential analysis tool for both theoretical and experimental chemists since accurate hybrid functionals were developed. Here we propose a local hybrid method derived from the optimized effective…
Orbital-free Density Functional Theory (OF-DFT) has been used when studying atoms, molecules and solids. In nuclear physics, there has been basically no application of OF-DFT so far, as the Density Functional Theory (DFT) has been widely…
We study the estimation, in Lp-norm, of density functions defined on [0,1]^d. We construct a new family of kernel density estimators that do not suffer from the so-called boundary bias problem and we propose a data-driven procedure based on…
We visualize the Kohn-Sham kinetic energy density (KED), and the ingredients -- the electron density, its gradient and Laplacian -- used to construct orbital-free models of it, for the AE6 test set of molecules. These are compared to…
Model-free reinforcement learning attempts to find an optimal control action for an unknown dynamical system by directly searching over the parameter space of controllers. The convergence behavior and statistical properties of these…
A systematic strategy for the calculation of density functionals (DFs) consists in coding informations about the density and the energy into polynomials of the degrees of freedom of wave functions. DFs and Kohn-Sham potentials (KSPs) are…
We discuss the physical properties and accuracy of three distinct dynamical (ie, frequency-dependent) kernels for the computation of optical excitations within linear response theory: i) an a priori built kernel inspired by the dressed…
Model degrees of freedom ($\df$) is a fundamental concept in statistics because it quantifies the flexibility of a fitting procedure and is indispensable in model selection. To investigate the gap between $\df$ and the number of independent…
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…