Related papers: Discretization of Continuous Frames by Quasi-Monte…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
The present work aims at the application of finite element discretizations to a class of equilibrium problems involving moving constraints. Therefore, a Moreau--Yosida based regularization technique, controlled by a parameter, is discussed…
This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…
A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least…
Continuous level Monte Carlo is an unbiased, continuous version of the celebrated multilevel Monte Carlo method. The approximation level is assumed to be continuous resulting in a stochastic process describing the quantity of interest.…
This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current…
The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. We use recent general results on sampling discretization to derive a new Marcinkiewicz type discretization theorem for the…
A discrete frame for $L^2({\mathbb R}^d)$ is a countable sequence $\{e_j\}_{j\in J}$ in $L^2({\mathbb R}^d)$ together with real constants $0<A\leq B< \infty$ such that $$ A\|f\|_2^2 \leq \sum_{j\in J}|\langle f,e_j \rangle |^2 \leq…
Estimating predictive uncertainty is crucial for many computer vision tasks, from image classification to autonomous driving systems. Hamiltonian Monte Carlo (HMC) is an sampling method for performing Bayesian inference. On the other hand,…
In this paper, we study the asymptotic error distribution for a two-level irregular discretization scheme of the solution to the stochastic differential equations (SDE for short) driven by a continuous semimartingale and obtain a central…
We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…
Given an $N$-dimensional subspace $X$ of $L_p([0,1])$, we consider the problem of choosing $M$-sampling points which may be used to discretely approximate the $L_p$ norm on the subspace. We are particularly interested in knowing when the…
Solving partial differential equations in high dimensions by deep neural network has brought significant attentions in recent years. In many scenarios, the loss function is defined as an integral over a high-dimensional domain. Monte-Carlo…
Techniques for evaluating the normalization integral of the target density for Markov Chain Monte Carlo algorithms are described and tested numerically. It is assumed that the Markov Chain algorithm has converged to the target distribution…
We propose a novel $hp$-multilevel Monte Carlo method for the quantification of uncertainties in the compressible Navier-Stokes equations, using the Discontinuous Galerkin method as deterministic solver. The multilevel approach exploits…
We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of quantum Monte Carlo data. With the sampled spectrum parametrized with delta-functions in continuous frequency space, a calculation of…
In this paper, we study the problem of sampling from log-concave distributions supported on convex, compact sets, with a particular focus on the randomized midpoint discretization of both vanilla and kinetic Langevin diffusions in this…
In the framework of uncertainty quantification, we consider a quantity of interest which depends non-smoothly on the high-dimensional parameter representing the uncertainty. We show that, in this situation, the multilevel Monte Carlo…
This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…
In this paper we present a general, axiomatical framework for the rigorous approximation of invariant densities and other important statistical features of dynamics. We approximate the system trough a finite element reduction, by composing…