相关论文: A Concentration Bound for Distributed Stochastic A…
Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…
This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element (FE) and domain decomposition (DD) methods. In addition to a fully parallel computation, the proposed lower bounds separate…
The problem of sampling a discrete-time sequence of spatially bandlimited fields with a bounded dynamic range, in a distributed, communication-constrained, processing environment is addressed. A central unit, having access to the data…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
The fundamental result of Li, Long, and Srinivasan on approximations of set systems has become a key tool across several communities such as learning theory, algorithms, computational geometry, combinatorics and data analysis. The goal of…
In this paper we propose a wide class of truncated stochastic approximation procedures with moving random bounds. While we believe that the proposed class of procedures will find its way to a wider range of applications, the main motivation…
In this paper, we first prove a high probability bound rather than an expectation bound for stochastic optimization with smooth loss. Furthermore, the existing analysis requires the knowledge of optimal classifier for tuning the step size…
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional…
Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method…
We derive novel concentration inequalities that bound the statistical error for a large class of stochastic optimization problems, focusing on the case of unbounded objective functions. Our derivations utilize the following key tools: 1) A…
This paper deals with the estimation of the distance between the solution of a static linear mechanic problem and its approximation by the finite element method solved with a non-overlapping domain decomposition method (FETI or BDD). We…
We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
In this work (Part I), we study three time-discretization procedures of the Dynamical Low-Rank Approximation (DLRA) of high-dimensional stochastic differential equations (SDEs). Specifically, we consider the Dynamically Orthogonal (DO)…
We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…
Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…
This paper considers distributed average consensus using finite-bit bounded quantizer with possibly unbounded data. Under the framework of the alternating direction method of multipliers (ADMM), we develop distributed averaging algorithms…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs),…
A generative model based on a continuous-time normalizing flow between any pair of base and target probability densities is proposed. The velocity field of this flow is inferred from the probability current of a time-dependent density that…