arXiv research

Study identifies and analyzes three types of errors in learning Fourier operators.

Unified error analysis for discrete flow models.

This work analyzes discrete diffusion models using stochastic integrals, providing error bounds and insights.

Derives EoM for DNNs to describe GD dynamics precisely.

First order discretizations of Langevin diffusion can achieve better generalization error with additional smoothness assumptions.

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 …

Corrected samplers reduce discretization error in discrete flow models without additional computational cost.

The paper analyzes the probabilistic structure of DDPMs and bounds their sampling error.

Study error bounds in evaluating distributional computational graphs.

New geometric SDEs and discretizations on Riemannian manifolds with error bounds.

We analyze the errors arising from discrete readjustment of the hedging portfolio when hedging options in exponential Levy models, and establish the rate at which the expected squared error goes to zero when the readjustment frequency increases. We compare the quadratic hedging strategy with the common market practice …

New estimators for intrinsic dimension and Wasserstein distance improve OT accuracy.

In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkhäuser/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize…

The paper analyzes errors in mechanical systems with external forces.

Bounds on factual and counterfactual distributions under measurement error in discrete models.

This work bounds the generalization error of private algorithms for discrete data.

MOB-dS uses permutation to correct for dependency in discrete survival data.

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

Paper optimizes clustering for multi-layer networks and discrete mixtures.

Continuous time framework for discrete data denoising models.

We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequentl…

New algorithm learns changing discrete distributions with minimal drift error.

New framework for discrete-state diffusion models reduces sample complexity.

Gradient-based methods for games suffer from discrete update steps that cause drift, affecting performance.

DFM models are analyzed for generating distributions with provable convergence.

This note clarifies connections between Föllmer process and DDPM sampler.

Accelerates convergence in global non-convex optimization with reversible diffusion.

We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.

ReDi improves few-step generation for discrete data models.

Discrete Gaussian noise preserves privacy and accuracy in differential privacy.

Study on error rates for approximating rough volatility models.

Discrete approximation solves Björling's minimal surface problem.

Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space the time-discret…

Proposes a method to quantify uncertainty in DNN models for discrete inputs.

In this paper, we will give a rigorous construction of the exact discrete Lagrangian formulation associated to a continuous Lagrangian problem. Moreover, we work in the setting of Lie groupoids and Lie algebroids which is enough general to simultaneously cover several cases of interest in discrete and continuous descri…

The paper analyzes sampling and estimation on manifolds using Langevin diffusion.

We present a numerical scheme to calculate fluctuation identities for exponential Lévy processes in the continuous monitoring case. This includes the Spitzer identities for touching a single upper or lower barrier, and the more difficult case of the two-barriers exit problem. These identities are given in the Fourier-L…

New method reduces bias in estimating causal effects from discretized variables.

Discrete time hedging in a complete diffusion market is considered. The hedge portfolio is rebalanced when the absolute difference between delta of the hedge portfolio and the derivative contract reaches a threshold level. The rate of convergence of the expected squared hedging error as the threshold level approaches z…

The paper tackles fast rates in structured prediction problems.

Optimal SQ bounds for learning binary product distributions and Ising models.

Replica exchange Langevin diffusion accelerates nonconvex optimization.

New insights into RL efficiency from managing time discretization.

Bayesian method improves segmentation accuracy with noisy labels.

Improved analysis for diffusion models reduces KL divergence error dependence on data dimension and discretization step size.

This article presents a finite element method (FEM) for a partial integro-differential equation (PIDE) to price two-asset options with underlying price processes modeled by an exponential Levy process. We provide a variational formulation in a weighted Sobolev space, and establish existence and uniqueness of the FEM-ba…

New algorithm estimates intrinsic dimension of discrete datasets.

Training classification models on imbalanced data tends to result in bias towards the majority class. In this paper, we demonstrate how variable discretization and cost-sensitive logistic regression help mitigate this bias on an imbalanced credit scoring dataset, and further show the application of the variable discret…