arXiv research

DeepONet accelerates reliability analysis of stochastic nonlinear systems.

Improved privacy analysis for stochastic gradient descent.

Derives effective continuous dynamics for adaptive SGD methods.

Identifies most probable flows for Kunita SDEs in fluid dynamics.

Stochastic stability is a popular solution concept for stochastic learning dynamics in games. However, a critical limitation of this solution concept is its inability to distinguish between different learning rules that lead to the same steady-state behavior. We address this limitation for the first time and develop a …

Improved convergence for non-log-concave sampling.

We present a unified framework to analyze the global convergence of Langevin dynamics based algorithms for nonconvex finite-sum optimization with $n$ component functions. At the core of our analysis is a direct analysis of the ergodicity of the numerical approximations to Langevin dynamics, which leads to faster conver…

Stochastic gradient methods converge for training wide PINNs.

NSGLD improves SGLD for non-convex optimization problems.

Optimal insurance and investment strategy under exponential preferences in a correlated market model.

Analysis of SGD for Gaussian mixture classification using dynamical mean-field theory.

MAntRA combines machine learning and Bayesian methods for time-dependent reliability analysis of unknown systems.

New rates for GLD and SGLD in infinite-dimensional spaces without dimensionality issues.

Efficient algorithm for unknown linear systems with convex costs.

Novel F2NARX model improves surrogate modeling for stochastic dynamical systems.

The paper analyzes error propagation in dynamic programming for stochastic control and option pricing.

Unified analysis of stochastic ADMM variants via SME.

Stochastic gradient Langevin dynamics (SGLD) is a fundamental algorithm in stochastic optimization. Recent work by Zhang et al. [2017] presents an analysis for the hitting time of SGLD for the first and second order stationary points. The proof in Zhang et al. [2017] is a two-stage procedure through bounding the Cheege…

The paper models market crashes as phase transitions, finding dynamic transitions offer better predictions.

Improved error estimate for SGLD sampling algorithm.

Many recent Markov chain Monte Carlo (MCMC) samplers leverage continuous dynamics to define a transition kernel that efficiently explores a target distribution. In tandem, a focus has been on devising scalable variants that subsample the data and use stochastic gradients in place of full-data gradients in the dynamic s…

Paper introduces a new volatility model for natural gas markets and discusses swing option pricing.

Adaptive neural network approximates stochastic system densities.

Dynamic skewness models improve financial time series analysis.

We propose a method to infer stochastic low-rank RNNs from neural data.

Stochastic Gradient Langevin Dynamics (SGLD) is a popular variant of Stochastic Gradient Descent, where properly scaled isotropic Gaussian noise is added to an unbiased estimate of the gradient at each iteration. This modest change allows SGLD to escape local minima and suffices to guarantee asymptotic convergence to g…

New RL algorithms correct bias in dynamic data analysis.

A new algorithm flattens multi-modal distributions for better deep learning.

This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic dynamics in a distribution-free manner. The new tools enjoy sound theory rooted in f…

This work examines the stability of GD and SGD near minima, revealing nonlinear dynamics that differ from linear analysis.

The paper introduces Causal Neural Operators to approximate operators in stochastic analysis.

HA-SME models SGD dynamics with Hessian info for better escaping behaviors.

Machine learning infers time-reversible dynamics from data.

Paper analyzes PSGLD for adaptive IRL with finite-sample bounds.

Method extracts governing laws from non-Gaussian stochastic systems data.

Develops robust methods for infinite-dimensional stochastic processes.

Improved KLMC for sampling under various conditions.

A new method optimizes knot selection for spline dimensional decomposition in stochastic dynamic analysis.

We consider the problem of sampling from a target distribution, which is \emph {not necessarily logconcave}, in the context of empirical risk minimization and stochastic optimization as presented in Raginsky et al. (2017). Non-asymptotic analysis results are established in the $L^1$-Wasserstein distance for the behavio…

Novel approach analyzes ReLU networks' training dynamics and proposes GmP for improved optimization.

GDM models time series with smoother transitions and interpretable states.

This paper investigates asymptotic behaviors of gradient descent algorithms (particularly accelerated gradient descent and stochastic gradient descent) in the context of stochastic optimization arising in statistics and machine learning where objective functions are estimated from available data. We show that these alg…

The paper develops a new probabilistic framework for denoising diffusion models using free entropy and stochastic analysis.

Foundational brain dynamics model using stochastic optimal control.

We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical stability as well as transitions between different stable states are found. This comb…

Paper analyzes online tensorial ICA convergence with stochastic approximation.

New framework analyzes SGD dynamics in large samples and dimensions.

The paper shows how label noise in training can lead to solutions that solve a Lasso program.