Weidong Liu's Homepage

Distinguished Professor
School of Mathematical Sciences
Shanghai Jiao Tong University
800 Dongchuan Road
Minhang, Shanghai

E-mail: weidongl@sjtu.edu.cn

• 2011-- Professor, School of Mathematical Sciences and Institute of Natural Sciences, Shanghai Jiao Tong University
• 2009--2011 Postdoctoral Fellow, Department of Statistics, The Wharton SchoolUniversity of Pennsylvania
• 2008--2009 Postdoctoral Fellow, Department of Mathematics, Hong Kong University of Science and Technology
• 2003--2008 Ph.D. in Mathematics, Zhejiang University, P.R. China

Honors and Awards

• National Excellent Doctoral Dissertation Award from China, 2010
• New World Mathematics Awards, Silver Award for the Ph.D Thesis, 2010.

Current Research Interests

• Modern statistics
• Machine learning

Publications (by subject)

Machine learning

• 1. Wang, X., Chen, X., Lin, Q. and Liu, W.D. (2020). Bayesian Decision Process for Budget-efficient Crowdsourced Clustering. International Joint Conferences on Artificial Intelligence, 2020.
• 2. Wang, X., Yang, Z., Chen, X. and Liu, W.D. (2019). Distributed Inference for Linear Support Vector Machine. Journal of Machine Learning Research, 20(113), 1-41.
• 3. Liu, W.D., Mao, X., Wong, R. (2020).Median matrix completion: from Embarrassment to optimality. The 37th International Conference on Machine Learning.
• 4. Chen, X., Liu, W.D. and Zhang, Y. (2019). Quantile Regression under Memory Constraint. Annals of Statistics, 47 (6), 3244-3273.
• 5. Xi Chen, Weidong Liu, Xiaojun Mao, and Zhuoyi Yang. (2020). Distributed High-dimensional Regression Under a Quantile Loss Function. Journal of Machine Learning Research, to appear.
• 6. Xi Chen, Weidong Liu and Xiaojun Mao (2020). Robust reduced rank regression in a distributed setting. Science China-Mathematics, to appear.
• 7. Chen, X., Liu, W.D. and Zhang, Y. (2019). First-order Newton-type Estimator for Distributed Estimation and Inference. Technical report.ARXIV
• 8. Tu, J.,Liu, W.D., Mao, X., Chen, X.(2020). Variance reduced median-of means estimator for Byzantine-robust distributed inference. Technical report.
• 9. Tu, J.,Liu, W.D., Mao, X.(2020). Byzantine-robust distributed sparse learning for M-estimation. Technical report.



Invariance principle under dependence

• 1. Liu, W.D. (2018). Gaussian approximations for weighted empirical processes under dependence. Technical report. [pdf]
• 2. Istvan Berkes, Weidong Liu and Wei Biao Wu (2014),Komlos-Major-Tusnady approximation under dependence. Annals of Probability, 42, 794-817. [pdf]
• 3. Liu, W.D., Chan, N. and Wang, Q. (2014). Uniform approximation to local time with applications in non-linear cointegrating regression. Published in a book by Wang, Q. [pdf]
• 4. Liu, W.D., Ling, S. and Shao, Q.M. (2011), On non-stationary threshold autoregressive models. Bernoulli. 17: 969-986.
• 5. Liu, W.D. and Lin, Z.Y. (2009), Strong approximation for a class of stationary processes, Stochastic Processes and their Applications,119: 249-280. [pdf]



Graphical models/linear regression/t tests with false discovery rate control and application

• 1. Liu, W.D., Leung, D. and Shao, Q.M. (2018). False discovery control for pairwise comparisons - an asymptotic solution to Williams, Jones and Tukey's conjecture. Technical report. [pdf]
• 2. Chen X. and Liu, W.D. (2017). Statistical inference for matrix-variate Gaussian graphical models and false discovery rate control. Statistica Sinica, to appear.
• 3. Liu, W.D. (2017). Structural similarity and difference testing on multiple sparse Gaussian graphical models. Annals of Statistics, to appear. [matlab code]
• 4. Cai, T. and Liu, W.D. (2016), Large-Scale Multiple Testing of Correlations. Journal of the American Statistical Association, 111, 229-240.[pdf]
• 5. Liu, W.D. (2014), Incorporation of Sparsity Information in Large-scale Multiple Two-sample t Tests. Technical report. [pdf] [matlab code] [matlab code]
• 6. Liu, W.D. and Luo, S. (2014), Hypothesis Testing for High-dimensional Regression Models. Technical report. [pdf]
• 7. Liu, W.D. and Shao, Q.M. (2014), Phase Transition and Regularized Bootstrap in Large-scale t-tests with False Discovery Rate Control. Annals of Statistics, 42, 2003-2025. [matlab code]
• 8. Liu, W.D. (2013), Gaussian Graphical Model Estimation with False Discovery Rate Control. Annals of Statistics, 41, 2948-2978. [matlab code]
• 9. Liao, K. MD, Sparks, J., Hejblum, B., Kuo, I., Cui, J., Lahey, L., Cagan, A., Gainer, V., Liu, W.D., Cai, T.T., Sokolove, J.,Cai, T. (2017). Phenome-wide association study of autoantibodies to citrullinated and non-citrullinated epitopes in rheumatoid arthritis. Arthritis & Rheumatology, 69, 742-749.



The (inverse) covariance matrix estimation and classification

• 1. Cai, T., Liu, W.D. and Zhou, H.B. (2016), Estimating Sparse Precision Matrix: Optimal Rates of Convergence and Adaptive Estimation. Annals of Statistics, 44, 455-488.
• 2. Cai, T., Cappola, T., Li, H., Liu, W.D. and Xie, J. (2016), Joint Estimation of Multiple High-dimensional Precision Matrices. Statistica Sinica, 26, 445-464.
• 3. Liu, W.D. and Luo, X. (2015), Fast and adaptive sparse precision matrix estimation in high dimensions. Journal of Multivariate Analysis, 135, 153-162
• 4. Tony Cai, Hongzhe Li, Weidong Liu, and Jichun Xie (2013),Covariate Adjusted Precision Matrix Estimation with an Application in Genetical Genomics. Biometrika, 100: 139-156. [pdf]
• 5. Cai, T. and Liu, W.D. (2011), A Direct Estimation Approach to Sparse Linear Discriminant Analysis. Journal of the American Statistical Association. 106: 1566-1577. [pdf] [matlab code]
• 6. Cai, T.,Liu, W.D. and Luo, X. (2011), A constrained L1 minimization approachto sparse precision matrix estimation. Journal of the American Statistical Association. 106: 594-607. [pdf]
• 7. Cai, T. and Liu, W.D. (2011), Adaptive thresholding for sparse covariance matrix estimation. Journal of the American Statistical Association. 106: 672-684.(with correction in the proof) [pdf][correction] [matlab code]



Various maximum type statistics with applications to global testing and inference


The most difficult aspect for the maximum type statistics is deriving their distributions under dependence. The main techniques in these works can be traced back to Liu, Lin and Shao (2008,AAP),Lin and Liu (2009, AOS), Liu and Wu (2010, ET,AOS).


• 1. Cao,H., Liu, W.D. and Zhou, Z. (2017). Simultaneous nonparametric regression analysis of sparse longitudinal data. Bernoulli, to appear.
• 2. Chen, X. and Liu, W.D. (2017). Testing independence with high-dimensional correlated samples. Annals of Statistics, to appear.
• 3. Degui Li, Weidong Liu, Qiying Wang and Weibiao Wu (2016),Simultaneous Inference for Nonlinear Cointegration Models. Statistica Sinica, to appear.
• 4. Tony Cai, Weidong Liu and Yin Xia (2014),Two-Sample Test of High Dimensional Means under Dependency. Journal of the Royal Statistical Society - Series B, 76, 349-372.
• 5. Tony Cai, Weidong Liu and Yin Xia (2013),Two-Sample Covariance Matrix Testing And Support Recovery in High-dimensional and Sparse Settings. Journal of the American Statistical Association, 108: 265-277. [pdf] [Supplement]
• 6. Liu, W.D. and Wu, W.B. (2010), Simultaneous nonparametric inference of time series. The Annals of Statistics. 38: 2388-2421. [pdf]
• 7. Liu, W.D. and Wu, W.B. (2010). Asymptotics of spectral density estimates. Econometric Theory. 26: 1218-1245. [pdf]
• 8. Li, D.L., Liu, W.D. and Rosalsky, A. (2010). Necessary and sufficient conditions for the asymptotic distribution of the largest entry of a sample correlation matrix. Probability Theory and Related Fields. 148: 5-35. [pdf]
• 9. Lin, Z.Y. and Liu, W.D. (2009), On maxima of periodograms of stationary processes, The Annals of Statistics, 37:2676-2695. [pdf]
• 10. Liu, W.D., Lin, Z.Y. and Shao, Q.M. (2008), The asymptotic distribution and Berry-Esseen bound of a new test for independence in high dimension with an application to stochastic optimization, The Annals of Applied Probability, 18: 2337-2366. [pdf]



Self-normalized limiting theorem

• 1. Weidong Liu and Qiman Shao (2013),A Cramer moderate deviation theorem for Hotelling T2-statistic with applications to global tests. Annals of Statistics, 41: 296-322.
• 2. Liu, W.D., Shao, Q.M. and Wang, Q. (2013), Self-normalized Cram\'{e}r type large deviations for the maximum of sums of independent random variables. Bernoulli, 19, 1006-1027. [pdf]
• 3. Liu, W.D. and Shao, Q.M. (2010), Cramer type moderate deviation for the maximum of the periodogram with application to simultaneous tests. The Annals of Statistics. 38: 1913-1935. [pdf]

Summer course on high dimensional statistical inference by Tony Cai and Ming Yuan, July 8-13, 2013

• summer course [pdf]

Links

• Job openings, faculty position of statistics in SJTU