Research

My research focuses on analysis and development of algorithms for high-dimensional sampling and uncertainty quantification, with applications in Bayesian inference, inverse problems, and generative modeling. I am currently developing localization methods for sampling that utilize graphical locality to reduce computational and statistical complexity. I also work on ensemble Kalman methods for high-dimensional inference and data assimilation. I am broadly interested in stochastic algorithms for high-dimensional problems.

Publications

• Spectral gap of Metropolis algorithms for non-smooth distributions under isoperimetry
  Shuigen Liu and Xin T. Tong, Japanese Journal of Statistics and Data Science, (2026). [arXiv:2601.21763]

• Localized diffusion models
  Georg A. Gottwald, Shuigen Liu, Youssef Marzouk, Sebastian Reich, and Xin T. Tong, (2026). Submitted to Bernoulli. [arXiv:2505.04417]

• Stein’s method for marginals on large graphical models
  Tiangan Cui, Shuigen Liu, and Xin T. Tong, (2026). Submitted to Bernoulli. [arXiv:2410.11771]

• Estimate of Koopman modes and eigenvalues with Kalman filter
  Ningxin Liu, Shuigen Liu, Xin T. Tong, and Lijian Jiang, SIAM Journal on Scientific Computing, 48 (2026), pp. A512–A539. [arXiv:2410.02815]

• Local MALA-within-Gibbs for Bayesian image deblurring with total variation prior
  Rafael Flock, Shuigen Liu, Yiqiu Dong, and Xin T. Tong, SIAM Journal on Scientific Computing, 47 (2025), pp. A2127–A2153. [arXiv:2409.09810]

• Dropout ensemble Kalman inversion for high dimensional inverse problems
  Shuigen Liu, Sebastian Reich, and Xin T. Tong, SIAM Journal on Numerical Analysis, 63 (2025), pp. 685–715. [arXiv:2308.16784]