77 citations · 198 across the 22 of their papers we have counts for
24 papers
Dropout Ensemble Kalman inversion for high dimensional inverse problems
Shuigen Liu, Sebastian Reich, Xin T. Tong
Ensemble Kalman inversion (EKI) is an ensemble-based method to solve inverse problems. Its gradient-free formulation makes it an attractive tool for problems with involved formulat…
Uniform error bound for PCA matrix denoising
Xin T. Tong, Wanjie Wang, Yuguan Wang
Principal component analysis (PCA) is a simple and popular tool for processing high-dimensional data. We investigate its effectiveness for matrix denoising. We consider the clean d…
Convergence Speed and Approximation Accuracy of Numerical MCMC
Tiangang Cui, Jing Dong, Ajay Jasra +1
When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how perturbation of MCMC affects t…
Stochastic Gradient Descent with Dependent Data for Offline Reinforcement Learning
Jing Dong, Xin T. Tong
In reinforcement learning (RL), offline learning decoupled learning from data collection and is useful in dealing with exploration-exploitation tradeoff and enables data reuse in m…
Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion
Simon Weissmann, Neil K. Chada, Claudia Schillings +1
Ensemble Kalman inversion (EKI) is a derivative-free optimizer aimed at solving inverse problems, taking motivation from the celebrated ensemble Kalman filter. The purpose of this…
Exploration Enhancement of Nature-Inspired Swarm-based Optimization Algorithms
Kwok Pui Choi, Enzio Hai Hong Kam, Tze Leung Lai +2
Nature-inspired swarm-based algorithms have been widely applied to tackle high-dimensional and complex optimization problems across many disciplines. They are general purpose optim…
Spectral Gap of Replica Exchange Langevin Diffusion on Mixture Distributions
Jing Dong, Xin T. Tong
Langevin diffusion (LD) is one of the main workhorses for sampling problems. However, its convergence rate can be significantly reduced if the target distribution is a mixture of m…
Consistency analysis of bilevel data-driven learning in inverse problems
Neil K. Chada, Claudia Schillings, Xin T. Tong +1
One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization,…
Dimension Independent Generalization Error by Stochastic Gradient Descent
Xi Chen, Qiang Liu, Xin T. Tong
One classical canon of statistics is that large models are prone to overfitting, and model selection procedures are necessary for high dimensional data. However, many overparameter…
Replica Exchange for Non-Convex Optimization
Jing Dong, Xin T. Tong
Gradient descent (GD) is known to converge quickly for convex objective functions, but it can be trapped at local minima. On the other hand, Langevin dynamics (LD) can explore the…
Convergence Acceleration of Ensemble Kalman Inversion in Nonlinear Settings
Neil K. Chada, Xin T. Tong
Many data-science problems can be formulated as an inverse problem, where the parameters are estimated by minimizing a proper loss function. When complicated black-box models are i…
Analysis of a localised nonlinear Ensemble Kalman Bucy Filter with complete and accurate observations
Jana de Wiljes, Xin T. Tong
Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with ph…
Accelerating Metropolis-within-Gibbs sampler with localized computations of differential equations
Qiang Liu, Xin T. Tong
Inverse problem is ubiquitous in science and engineering, and Bayesian methodologies are often used to infer the underlying parameters. For high dimensional temporal-spatial models…
On Stationary-Point Hitting Time and Ergodicity of Stochastic Gradient Langevin Dynamics
Xi Chen, Simon S. Du, Xin T. Tong
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…
Tikhonov Regularization Within Ensemble Kalman Inversion
Neil K. Chada, Andrew M. Stuart, Xin T. Tong
Ensemble Kalman inversion is a parallelizable methodology for solving inverse or parameter estimation problems. Although it is based on ideas from Kalman filtering, it may be viewe…
Spatial localization for nonlinear dynamical stochastic models for excitable media
Nan Chen, Andrew J. Majda, Xin T. Tong
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are o…
Simple Nonlinear Models with Rigorous Extreme Events and Heavy Tails
Andrew J. Majda, Xin T. Tong
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochast…
Rigorous Analysis for Efficient Statistically Accurate Algorithms for Solving Fokker-Planck Equations in Large Dimensions
Nan Chen, Andrew J. Majda, Xin T. Tong
This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbule…
Performance analysis of local ensemble Kalman filter
Xin T. Tong
Ensemble Kalman filter (EnKF) is an important data assimilation method for high dimensional geophysical systems. Efficient implementation of EnKF in practice often involves the loc…
Statistical Inference for Model Parameters in Stochastic Gradient Descent
Xi Chen, Jason D. Lee, Xin T. Tong +1
The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most exist…
Rigorous accuracy and robustness analysis for two-scale reduced random Kalman filters in high dimensions
Andrew J. Majda, Xin T. Tong
Contemporary data assimilation often involves millions of prediction variables. The classical Kalman filter is no longer computationally feasible in such a high dimensional context…
Performance of Ensemble Kalman filters in large dimensions
Andrew J. Majda, Xin T. Tong
Contemporary data assimilation often involves more than a million prediction variables. Ensemble Kalman filters (EnKF) have been developed by geoscientists. They are successful ind…
Nonlinear stability of the ensemble Kalman filter with adaptive covariance inflation
Xin T Tong, Andrew J Majda, David Kelly
The Ensemble Kalman filter and Ensemble square root filters are data assimilation methods used to combine high dimensional nonlinear models with observed data. These methods have p…
Nonlinear stability and ergodicity of ensemble based Kalman filters
X. T. Tong, A. J. Majda, D. Kelly
The ensemble Kalman filter (EnKF) and ensemble square root filter (ESRF) are data assimilation methods used to combine high dimensional, nonlinear dynamical models with observed da…