arXiv research

GANs learn distributions well from samples, with rates depending on intrinsic dimension.

Formula found for neural network error with fixed weights.

We construct algorithms via binomial approximations for computation of prices of game put options and obtain estimates of approximation errors.

High-probability bound for distributed stochastic approximation tracking error.

The paper analyzes CycleGAN's error components for unpaired data generation.

Improved approximations for rough Heston model reduce errors.

This paper examines error bounds for deep learning classifiers with noisy labels.

Correction for Error estimates for binomial approximations of game options [math.PR/0607123]

This paper analyzes VAE approximation errors in conditional exponential families.

New bounds on ReLU networks for low-regular functions.

This study is aimed at answering the famous question of how the approximation errors at each iteration of Approximate Dynamic Programming (ADP) affect the quality of the final results considering the fact that errors at each iteration affect the next iteration. To this goal, convergence of Value Iteration scheme of ADP…

Deep neural networks approximate functions in shift-invariant spaces with controlled error.

Asynchronous stochastic approximations (SAs) are an important class of model-free algorithms, tools and techniques that are popular in multi-agent and distributed control scenarios. To counter Bellman's curse of dimensionality, such algorithms are coupled with function approximations. Although the learning/ control pro…

We approximate derivatives of functions on manifolds by embedding them and applying vector-valued operators.

Deep learning method improves numerical approximation of FBSDEs with jumps.

Study analyzes error in ReLU networks with local connections.

Two new algorithms improve Q* approximation in batch RL with linear error propagation.

New fairness concept extends minimax fairness to lexicographic fairness.

Derives error bounds for stochastic iterative algorithms using Stein's method.

New method improves Euler approximation for local stochastic volatility models.

We consider in this paper the optimal approximations of convex univariate functions with feed-forward Relu neural networks. We are interested in the following question: what is the minimal approximation error given the number of approximating linear pieces? We establish the necessary and sufficient conditions and uniqu…

This study uses neural networks to approximate Bayesian filtering problems.

RQMC improves kernel-based learning by reducing deterministic error and offering computational advantages.

Many machine learning frameworks, such as resource-allocating networks, kernel-based methods, Gaussian processes, and radial-basis-function networks, require a sparsification scheme in order to address the online learning paradigm. For this purpose, several online sparsification criteria have been proposed to restrict …

Neural networks can approximate complex stochastic equations well.

Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem is to identify promising (explicit) features leading to a satisfactory out-of-sam…

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 mean-squared error attains a lower bound are constructed. Two applications are …

This paper develops a bootstrap method to estimate errors in Random Fourier Features.

We derive error estimates for multinomial approximations of American options in a multidimensional jump--diffusion Merton's model. We assume that the payoffs are Markovian and satisfy Lipschitz type conditions. Error estimates for such type of approximations were not obtained before. Our main tool is the strong approxi…

Study provides error estimates for approximating game options with diffusion asset prices.

Study shows limits on deep and shallow neural networks for approximating compact sets.

This paper establishes the (nearly) optimal approximation error characterization of deep rectified linear unit (ReLU) networks for smooth functions in terms of both width and depth simultaneously. To that end, we first prove that multivariate polynomials can be approximated by deep ReLU networks of width $\mathcal{O}(N…

The paper bounds neural networks' approximation error and applies it to regression and GANs.

Recently, artificial neural networks (ANNs) in conjunction with stochastic gradient descent optimization methods have been employed to approximately compute solutions of possibly rather high-dimensional partial differential equations (PDEs). Very recently, there have also been a number of rigorous mathematical results …

Improved COD algorithm reduces streaming AMM errors and uses less space.

This paper analyzes error bounds for biased SMC samplers in conditional sampling.

Theoretical analysis of entropy approximation for Gaussian mixtures.

We find approximate solutions of partial integro-differential equations, which arise in financial models when defaultable assets are described by general scalar Lévy-type stochastic processes. We derive rigorous error bounds for the approximate solutions. We also provide numerical examples illustrating the usefulness a…

Develops wavelet-based neural network approximation theory.

New error bounds for flow matching methods using deterministic sampling.

EBUCB framework achieves optimal regret with bounded approximate inference error.

Gaussian process regression helps approximate Bayesian inverse problems efficiently.

Study optimizes solving fixed-point equations using subspace search.

Study efficient neural operator learning using variation spaces.

Deep belief networks can approximate any multivariate density with binary hidden units.

Double Q-learning has the same mean-squared error as Q-learning under certain conditions.

Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty estimates. Classical Monte Carlo methods, particularly Markov Chain Monte Carlo, rem…

Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential equations into the theoretical framework of diffusion approximation, extending the …