Related papers: Gradient-based stochastic estimation of the densit…

Superconductors have been among the most fascinating substances, as the fundamental concept of superconductivity as well as the correlation of critical temperature and superconductive materials have been the focus of extensive investigation…

Density gradient theory (DGT) allows fast and accurate determination of surface tension and density profile through a phase interface. Several algorithms have been developed to apply this theory in practical calculations. While the…

Decentralized stochastic optimization has emerged as a fundamental paradigm for large-scale machine learning. However, practical implementations often rely on biased gradient estimators arising from communication compression or inexact…

We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…

This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…

In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that…

Latent variable models are powerful tools for modeling complex phenomena involving in particular partially observed data, unobserved variables or underlying complex unknown structures. Inference is often difficult due to the latent…

The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…

We propose to apply several gradient estimation techniques to enable the differentiation of programs with discrete randomness in High Energy Physics. Such programs are common in High Energy Physics due to the presence of branching processes…

Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a…

This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…

With the emergence of Artificial Intelligence, numerical algorithms are moving towards more approximate approaches. For methods such as PCA or diffusion maps, it is necessary to compute eigenvalues of a large matrix, which may also be dense…

Methods exhibiting linear scaling with respect to the size of the system, so called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms…

We study both systematic and statistical errors in radiation density matrix measurements. First we estimate the minimum number of scanning phases needed to reduce systematic errors below a fixed threshold. Then, we calculate the statistical…

We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…

The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention…

To compute the spatially distributed dielectric constant from the backscattering data, we study a coefficient inverse problem for a 1D hyperbolic equation. To solve the inverse problem, we establish a new version of Carleman estimate and…

In a recent Letter, Baer et al. present a stochastic method for Kohn-Sham density functional theory calculations. Their convergence criterion is the self-averaging total energy per electron, which requires a number of statistical samples…

Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are…

Methods for calculating an electron density of a periodic crystal constructed using non-orthogonal localised orbitals are discussed. We demonstrate that an existing method based on the matrix expansion of the inverse of the overlap matrix…