arXiv research

Finite approximations help reconstruct countable metric and ultrametric spaces.

New method for finite approximations improves inference efficiency and applicability.

The paper extends a theorem to number fields without infinite places.

Paper develops a finite dimensional approximation scheme for Riemannian manifolds.

Study finds the minimum number of finite Gaussian mixtures for best approximation.

We show that finite-width deep ReLU neural networks yield rate-distortion optimal approximation (Bölcskei et al., 2018) of polynomials, windowed sinusoidal functions, one-dimensional oscillatory textures, and the Weierstrass function, a fractal function which is continuous but nowhere differentiable. Together with thei…

We show in this note that the Sobolev Discrepancy introduced in Mroueh et al in the context of generative adversarial networks, is actually the weighted negative Sobolev norm $||.||_{\dot{H}^{-1}(ν_q)}$, that is known to linearize the Wasserstein $W_2$ distance and plays a fundamental role in the dynamic formulation of…

An approximation theorem for minimal surfaces by complete minimal surfaces of finite total curvature in $\mathbb{R}^3$ is obtained. This Mergelyan type result can be extended to the family of complete minimal surfaces of weak finite total curvature, that is to say, having finite total curvature on proper regions of fin…

In this paper we study the problem of approximation of the $L^2$-topological invariants by their finite dimensional analogues. We obtain generalizations of the theorem of Lück, dealing with towers of finitely sheeted normal coverings. We prove approximation theorems, establishing relations between the homological invar…

The paper analyzes finite element methods on manifolds with approximate metrics.

The paper clarifies the approximation of SGD with Ito SDEs for finite learning rates.

Study on stable translation lengths of surface homeomorphisms and their approximations.

Investigates the impact of finite VC dimension on neural network approximation and learning.

This paper analyzes momentum Q-learning with finite-sample guarantees.

Finite-gap solutions approximate jets of initial data for certain BKM systems.

New algorithms for approximating stochastic processes efficiently.

The study establishes equivalence of conditions on metric manifolds with finite volume.

We show that the sets in a family with finite VC dimension can be uniformly approximated within a given error by a finite partition. Immediate corollaries include the fact that VC classes have finite bracketing numbers, satisfy uniform laws of averages under strong dependence, and exhibit uniform mixing. Our results ar…

Finite difference approximations to multi-asset American put option price are considered. The assets are modelled as a multi-dimensional diffusion process with variable drift and volatility. Approximation error of order one quarter with respect to the time discretisation parameter and one half with respect to the space…

Study Gaussian approximation for deep neural networks with random weights.

The study optimizes Gaussian process approximations for finite-rank models.

The paper improves convergence rates of curvature approximations using Regge elements.

Detect changes in noisy dynamical systems using empirical approximations and finite-sample bounds.

The paper approximates Levi-Civita connection and curvature on 2D manifolds using finite elements.

The aim of this paper is to show how the homotopy type of compact metric spaces can be reconstructed by the inverse limit of an inverse sequence of finite approximations of the corresponding space. This recovering allows us to define inverse persistence as a new kind of persistence process.

Paper solves convertible bond valuation using finite elements with penalty method.

Q-learning with neural network function approximation (neural Q-learning for short) is among the most prevalent deep reinforcement learning algorithms. Despite its empirical success, the non-asymptotic convergence rate of neural Q-learning remains virtually unknown. In this paper, we present a finite-time analysis of a…

The paper approximates Einstein tensor using finite elements.

New algorithms minimize regret in SSP with optimal sparse updates.

The paper improves PCS approximation for ranking and selection under limited simulation budgets.

Improved bounds for neural network approximations of functions.

Paper analyzes Greedy-GQ for reinforcement learning with Markovian noise.

Paper analyzes online tensorial ICA convergence with stochastic approximation.

We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2 . The class includes, as a special case, the usual empirical norm encountered, for example, in the context of nonparametric regression in reproduci…

A recent paper of Arnold, Falk, and Winther [Bull AMS, 47 (2010)] showed that a large class of mixed finite element methods can be formulated naturally on Hilbert complexes, where using a Galerkin-like approach, one solves a variational problem on a finite-dimensional subcomplex. In a seemingly unrelated research direc…

We solve POMDPs by approximating them as finite-state MDPs.

This work analyzes nonexpansive stochastic approximations with Markovian noise, proving convergence in reinforcement learning.

First-order method solves stochastic bilevel optimization with linear constraints.

The study of universal approximation of arbitrary functions $f: \mathcal{X} \to \mathcal{Y}$ by neural networks has a rich and thorough history dating back to Kolmogorov (1957). In the case of learning finite dimensional maps, many authors have shown various forms of the universality of both fixed depth and fixed width…

Study on SA with heavy-tailed and LRD noise, establishing finite-time bounds.

We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average process based on a truncated Laguerre series expansion. The resulting problem is a fin…

Improves Laplace approximation for Bayesian inference on Riemannian manifolds.

This study approximates distances between Gaussian processes and covariance operators using RKHS.

Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian variables and the first two posterior moments of the two generating variables (corre…

New methods stabilize Q-learning with linear approximations.

Study on distributional TD learning with linear approximations for better return estimation.

Locally approximating groups of homeomorphisms reveal manifold properties.

Gaussian processes (GPs) offer a flexible class of priors for nonparametric Bayesian regression, but popular GP posterior inference methods are typically prohibitively slow or lack desirable finite-data guarantees on quality. We develop an approach to scalable approximate GP regression with finite-data guarantees on th…