Related papers: Approximating with Gaussians
Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…
Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB…
The density distribution in solids is often represented as a sum of Gaussian peaks (or similar functions) centred on lattice sites or via a Fourier sum. Here, we argue that representing instead the $\mathit{logarithm}$ of the density…
Formulas are derived for the average level density of deformed, or transition, Gaussian orthogonal random matrix ensembles. After some general considerations about Gaussian ensembles we derive formulas for the average level density for (i)…
We consider the problem of approximating two, possibly unrelated probability distributions from a single complex-valued function $\psi$ and its Fourier transform. We show that this problem always has a solution within a specified degree of…
A general procedure for the optimization of atomic density-fitting basis functions is designed with the balance between accuracy and numerical stability in mind. Given one-electron wavefunctions and energies, weights are assigned to the…
Several problems on Fourier series and trigonometric approximation on a hexagon and a triangle are studied. The results include Abel and Ces\`aro summability of Fourier series, degree of approximation and best approximation by trigonometric…
The first paper in this series introduced a new approach to strong convergence of random matrices that is based primarily on soft arguments. This method was applied to achieve a refined qualitative and quantitative understanding of strong…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
We analyse three related preconditioned steepest descent algorithms, which are partially popular in Hartree-Fock and Kohn-Sham theory as well as invariant subspace computations, from the viewpoint of minimization of the corresponding…
Fourier series approximations of continuous but nonperiodic functions on an interval suffer the Gibbs phenomenon, which means there is a permanent oscillatory overshoot in the neighbourhoods of the endpoints. Fourier extensions circumvent…
Locally weighted regression was created as a nonparametric learning method that is computationally efficient, can learn from very large amounts of data and add data incrementally. An interesting feature of locally weighted regression is…
A Poincar\'{e} gauge theory of (2+1)-dimensional gravity is developed. Fundamental gravitational field variables are dreibein fields and Lorentz gauge potentials, and the theory is underlain with the Riemann-Cartan space-time. The most…
This work brings together two powerful concepts in Gaussian processes: the variational approach to sparse approximation and the spectral representation of Gaussian processes. This gives rise to an approximation that inherits the benefits of…
In this contribution we deal with Gaussian quadrature rules based on orthogonal polynomials associated with a weight function $w(x)= x^{\alpha} e^{-x}$ supported on an interval $(0,z)$, $z>0.$ The modified Chebyshev algorithm is used in…
This paper develops the theory and methods for modeling a stationary count time series via Gaussian transformations. The techniques use a latent Gaussian process and a distributional transformation to construct stationary series with very…
We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…
We consider a nearly Gaussian random variable $X$ (see \cite{Lefebvre}) that, after a power transformation, the variable $X^c$ where $c=\{(2k+1)/(2j+1)\}$, $k,j=\{0,1,\dots\}$, is approximately Gaussian. This transformation is useful to…
We investigate the realizations of a random Gaussian field on a finite domain of ${\mathbb R}^d$ in the limit where a given linear functional of the field is large. We prove that if its variance is bounded, the field converges uniformly and…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…