Weak Convergence

Weak convergence, a concept describing the convergence of probability measures, is central to analyzing the behavior of complex systems, particularly in stochastic processes and machine learning. Current research focuses on extending weak convergence to account for temporal dependencies in stochastic processes (e.g., using high-rank path development) and analyzing the convergence of neural network algorithms (e.g., actor-critic methods and t-SNE) by relating them to ordinary differential equations. These advancements are crucial for establishing theoretical guarantees for machine learning models and improving the reliability of simulations involving stochastic processes, impacting fields like finance and time series analysis.

Papers

October 2, 2024

Approximation by Steklov Neural Network Operators
S. N. Karaman, M. Turgay, T. Acar
Neural Operator Average Approximation Convergence Analysis Weak Convergence

May 23, 2024

High Rank Path Development: an approach of learning the filtration of stochastic processes
Jiajie Tao, Hao Ni, Chong Liu
Constructive Approach C Gan Stochastic Process Weak Convergence Rough Path Path Development Pressure Filtration

March 25, 2024

Weak Convergence Analysis of Online Neural Actor-Critic Algorithms
Samuel Chun-Hei Lam, Justin Sirignano, Ziheng Wang
Neural Network Policy Gradient Actor Critic Algorithm Critic Model Weak Convergence Online Deep Learning

January 31, 2024

Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold
Seonghyeon Jeong, Hau-Tieng Wu
Point Cloud Gradient Flow Convergence Analysis Kullback Leibler Divergence SNE Algorithm Weak Convergence

September 8, 2023

Online Infinite-Dimensional Regression: Learning Linear Operators
Vinod Raman, Unique Subedi, Ambuj Tewari
P$ Norm Hilbert Space Uniform Convergence Weak Convergence Linear Operator

June 2, 2023

Uniform Convergence of Deep Neural Networks with Lipschitz Continuous Activation Functions and Variable Widths
Yuesheng Xu, Haizhang Zhang
Deep Neural Network Convergence Analysis Uniform Convergence Weak Convergence Lipschitz Activation Lipschitz Continuity Assumption

February 1, 2023

Gradient Descent in Neural Networks as Sequential Learning in RKBS
Alistair Shilton, Sunil Gupta, Santu Rana, Svetha Venkatesh
Neural Network Gradient Descent Neural Tangent Kernel Kernel Hilbert Space Sequential Learning Generalization Property Taylor Expansion Weak Convergence Kernel Banach Space

November 10, 2022

Controlling Moments with Kernel Stein Discrepancies
Heishiro Kanagawa, Alessandro Barp, Arthur Gretton, Lester Mackey
Convergence Analysis Temporal Moment Weak Convergence Kernel Stein Discrepancy Wasserstein 2 Stein Discrepancy

June 27, 2022

Supervised Learning with General Risk Functionals
Liu Leqi, Audrey Huang, Zachary C. Lipton, Kamyar Azizzadenesheli
Supervised Learning Empirical Risk Minimization Risk Minimization Uniform Convergence Weak Convergence

May 1, 2022

On the speed of uniform convergence in Mercer's theorem
Rustem Takhanov
Speed Effect Theorem Driven Question Positive Definite Kernel Weak Convergence Integral Operator Separable Kernel

December 8, 2021

Optimistic Rates: A Unifying Theory for Interpolation Learning and Regularization in Linear Regression
Lijia Zhou, Frederic Koehler, Danica J. Sutherland, Nathan Srebro
Linear Regression Unifying Theory Statistical Guarantee Fast Rate Weak Convergence Interpolation Learning Minimum Norm

November 21, 2021

PAC-Learning Uniform Ergodic Communicative Networks
Yihan He
Network Structure PAC Learning Rademacher Complexity High Probability Bound Weak Convergence

November 15, 2021

ELBD: Efficient score algorithm for feature selection on latent variables of VAE
Yiran Dong, Chuanhou Gao
Feature Selection Latent Variable Lung VAE Score Based Weak Convergence Evidence Lower Bound Gaussian Posterior

May 19, 2021

Diffusion Approximations for Thompson Sampling
Lin Fan, Peter W. Glynn
Thompson Sampling Sampling Based Algorithm Weak Convergence