Xin Tong

Research Interests

• Key Words: High dimension, Data assimilation, Stochastic process, Data analysis

My research interests lie broadly inside probability theory and its applications in statistics, machine learning and nonlinear systems. My recent research involves investigating the behavior of algorithms, e.g. EnKF, MCMC and SGD, when the problem dimension is high. One of the common theme is that we can show stable performance of these algorithms, if certain intrinsic structures can be exploited.

Education

• Doctor of Philosophy (PhD) Princeton University (2009 — 2013)
• Bachelor of Arts (BA) Peking University (2005 — 2009)

Companies

• Assistant Professor National University of Singapore (2016)
• Postdoctoral Associate New York University (2013 — 2016)

Publications

Optimization and sampling in machine learning

• Replica exchange Monte Carlo

  • Spectral gap of replica exchange Langevin diffusion on mixture distributions (with J. Dong). (2020)
    
  • Replica exchange for non-convex optimization (with J. Dong) . (2020)
    

• Meta-heuristic Optimization

  • Stability bounds and almost sure convergence of improved particle swarm optimization methods (with K. P. Choi, T. Lai and W. Wong) (2020)

• High dimensional machine learning

  • On Stationary-Point Hitting Time and Ergodicity of Stochastic Gradient Langevin Dynamics ( with X. Chen and S. S. Du) Journal of Machine Learning Research, 21(68):1−41, 2020
    
  • Statistical Inference for Model Parameters in Stochastic Gradient Descent, 2016, with with X. Chen, J. Lee and Y. Zhang. Ann. of Stat. 48 (1), 251-273 (2020)

Monte Carlo and inverse problems and machine learning

• Efficient MCMC sampler exploiting local structures

  • MALA-within-Gibbs samplers for high-dimensional distributions with sparse conditional structure (with M. Morzfeld, Y. Marzouk). (2019)
    
  • Localization for MCMC: sampling high-dimensional posterior distributions with banded structure (with M. Morzfeld, Y. Marzouk) accepted by Journal of computational physics. (2018) 33 pages

• Ensemble Kalman inversion

  • Consistency analysis of bilevel Data-driven learning in inverse problems (with N. Chada, C. Schillings and S. Weissmann)
  • Convergence Acceleration of Ensemble Kalman Inversion in Nonlinear Settings (with N. K. Chada)
  • Tikhonov Regularization within Ensemble Kalman Inversion (with N. K. Chada, A. M. Stuart)

Data Assimilation

• Performance analysis of Data assimilation methods

  • Analysis of a localised nonlinear Ensemble Kalman Bucy Filter with complete and accurate observations, (with J. de Wiljes )
    
  • Performance analysis of local ensemble Kalman filter, 2018 J. Nonlinear. Sci., 28(4), 1397-1442, 40 pages
  • Rigorous accuracy and robustness analysis for two-scale reduced random Kalman filters in high dimensions, 2018. With A.J. Majda. Comm. Pure Appl. Math., 71(5), 892-937
  • Robustness and Accuracy of finite Ensemble Kalman filters in large dimensions, 2018, with A. Majda. 42 pages.

• Stability of Ensemble Kalman filters

  • Nonlinear stability and ergodicity of ensemble based Kalman filters, 2016, with A. Majda and D. Kelly. Nonlinearity, 29(2), 657-691
  • Concrete ensemble Kalman filters with rigorous catastrophic filter divergence, 2015, with D. Kelly and A. Majda. Proc. Natl. Acad. Sci. USA., vol 112, no. 34, 10589-10594. (2015)
  • Nonlinear stability of ensemble Kalman filters with adaptive covariance inflation, 2016, with A. Majda and D. Kelly. Commun. Math. Sci. 14(5),1283-1313

• Filtering with Lagrangian data

  • Noisy Lagrangian Tracers for Filtering Random Rotating Compressible Flows, 2015, with N. Chen and A. Majda. J. Nonlinear Sci. V25, Issue 3, 451-488
  • Information Barriers for Noisy Lagrangian Tracers in Filtering Random Incompressible Flows, 2014, with N. Chen and A. Majda. Nonlinearity. V27, No. 9

• Ergodicity of nonlinear filters

  • Thesis: Filter Stability in Infinite Dimensional Systems, 2013. Supervised by R. van Handel
    
  • Conditional ergodicity in infinite dimension, 2014, with R. van Handel. Ann. Probab. V42, No. 6, 2243-2313
  • Ergodicity and stability of the conditional distributions of nondegenerate Markov chains, 2012, with R. van Handel. Ann. Appl. Probab. V22, No. 4, 1495-1540

Nonlinear stochastic models and Uncertainty Quantification

• Spatial localization phenomena

  • Spatial localization for nonlinear dynamical stochastic models for excitable media (with N. Chen and A. J. Majda) Chinese Annals of Mathematicatcs Series B, Volume 40, Number 6, 2019
    

• High dimensional uncertainty quantification for Fokker Plank equations

  • Rigorous Analysis for efficient statistically accurate algorithms for solving Fokker-Plank Equations in Large dimensions, 2018. (with N. Chen and A. J. Majda) SIAM/ASA Journal on Uncertainty Quantification 6 (3), 1198-1223

• Intermittency of nonlinear processes

  • Simple Nonlinear Models with Rigorous Extreme Events and Heavy Tails, 2018, with A. Majda. Accepted by Nonlinearity.
  • Moment bounds and geometric ergodicity of diffusions with random switching and unbounded transition rates, 2016 with A.J. Majda. Res. Math. Sci. 3(41), 2016
  • Intermittency in Turbulent Diffusion Models with a Mean Gradient, 2016, with A. Majda. Nonlinearity, 28(11), 4171-4208
    

• Ergodicity of stochastic turbulence

  • Ergodicity of Truncated Stochastic Navier Stokes with Deterministic Forcing and Dispersion, 2016, with A. Majda. J. Nonlinear Sci.,
  • Geometric Ergodicity for Piecewise Contracting Processes with Applications for Tropical Stochastic Lattice Models, 2016, with A. Majda. Comm. Pure Appl. Math. 69(6), 1110-1153