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My research is supported in part by NSF CAREER-1944904, NSF DMS-1811868, and NIH R01 GM131399.

Slides of recent work

• Optimal singular value decomposition for high-dimensional tensor data
• A fast and easy-to-implement second-order method for rank-constrained optimization & low-rank matrix recovery/completion
• Optimal and efficient tensor regression analysis via importance sketching
• Unilateral perturbation bound
• Semi-supervised inference

Discussions

• Discussion of ``Vintage factor analysis with Varimax performs statistical inference" (with Rungang Han).

Preprints awaiting publication :-)

• Learning polynomial transformations (with Sitan Chen, Jerry Li, and Yuanzhi Li)
• Guaranteed functional tensor singular value decomposition (with Rungang Han and Pixu Shi).
• On geometric connections of embedded and quotient geometries in Riemannian fixed-rank matrix optimization (with Yuetian Luo and Xudong Li).
• Nonconvex factorization and manifold formulations are almost equivalent in low-rank matrix optimization (with Yuetian Luo and Xudong Li).
• Exact clustering in tensor block model: Statistical optimality and computational limit (with Rungang Han, Yuetian Luo, and Miaoyan Wang). [R Package]
  (This paper received the Student's Paper Award from the Statistical Learning and Data Science Section of the American Statistical Association, 2021)
• Low-rank tensor estimation via Riemannian Gauss-Newton: Statistical optimality and second-order convergence (with Yuetian Luo).
• Recursive importance sketching for rank constrained least squares (with Yuetian Luo, Xudong Li, and Wen Huang).

Publications

• Inference for low-rank tensors -- No need to debias (with Dong Xia and Yuchen Zhou), The Annals of Statistics, to appear.
• On the non-asymptotic concentration of heteroskedastic Wishart-type matrix (with Tony Cai and Rungang Han), Electronic Journal of Probability, to appear.
• Optimal high-order tensor SVD via tensor-train orthogonal iteration (with Yuchen Zhou, Lili Zheng, and Yazhen Wang), IEEE Transactions on Information Theory, to appear. [R Package]
  
• Sparse Group Lasso: Optimal Sample Complexity, Convergence Rate, and Statistical Inference (with Tony Cai and Yuchen Zhou), IEEE Transactions on Information Theory, to appear.
• A Schatten-q low-rank matrix perturbation analysis via perturbation projection error bound (with Yuetian Luo and Rungang Han), Linear Algebra and Its Applications, 630, 225-240, 2021.
• Tensor clustering with planted structures: Statistical optimality and computational limits (with Yuetian Luo), The Annals of Statistics, to appear, 2021.
• An optimal statistical and computational framework for generalized tensor estimation (with Rungang Han and Rebecca Willett), The Annals of Statistics, to appear, 2021.
• A sharp blockwise tensor perturbation bound for orthogonal iteration (with Yuetian Luo, Garvesh Raskutti, and Ming Yuan), Journal of Machine Learning Research, 22, 1-48, 2021.
• Heteroskedastic PCA: Algorithm, optimality, and applications (with Tony Cai and Yihong Wu), The Annals of Statistics, to appear.
• High-dimensional log-error-in-variable regression with applications to microbial compositional data analysis (with Pixu Shi and Yuchen Zhou), Biometrika, to appear, 2021.
  (This paper received Biometrics Early-Stage Investigator Award by the Biometrics Section of the American Statistical Association, 2019)
• Learning good state and action representations via tractable tensor decomposition (with Chengzhuo Ni, Yaqi Duan and Mengdi Wang), International Symposium on Information Theory (ISIT), 2021.
• ISLET: fast and optimal low-rank tensor regression via importance sketchings (with Yuetian Luo, Garvesh Raskutti, and Ming Yuan), SIAM Journal on Mathematics of Data Science, 2, 444-479, 2020. [R package]
• Learning Markov models via low-rank optimization (with Ziwei Zhu, Xudong Li and Mengdi Wang), Operations Research, to appear.
• Nonparametric covariance estimation for mixed longitudinal studies, with applications in midlife women's health (with Kehui Chen), Statistica Sinica, 32, 345-365, 2022.
• Open problem: Average-case hardness of hypergraphic planted clique detection (with Yuetian Luo), Conference on Learning Theory (COLT), 125, 3852-3856, 2020. [talk and slides]
• On the non-asymptotic and sharp tail bounds of random variables (with Yuchen Zhou), Stat, 9, e314, 2020.
• Sparse and low-rank tensor estimation via cubic sketchings (with Botao Hao and Guang Cheng), IEEE Transactions on Information Theory, 66, 9, 2020.
  A short version published in Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), 2020.
• Multi-sample estimation of bacterial composition matrix in metagenomics data (with Yuanpei Cao and Hongzhe Li), Biometrika, 107, 75-92, 2020.
• Spectral state compression of Markov processes (with Mengdi Wang), IEEE Transactions on Information Theory, 66, 3202-3231, 2020.
• Cross: Efficient low-rank tensor completion (single author), The Annals of Statistics, 47, 936-964, 2019. [R package]
• Optimal sparse singular value decomposition for high-dimensional high-order data (with Rungang Han), Journal of American Statistical Association, 114, 1708-1725, 2019. [R package]
• Semi-supervised inference: General theory and estimation of means (with Lawrence Brown and Tony Cai), The Annals of Statistics, 47, 2538-2566, 2019.
• Tensor SVD: Statistical and computational limits (with Dong Xia), IEEE Transactions on Information Theory, 64, 1-28, 2018. [An R implementation]
• Sequential rerandomization (with Quan Zhou, Philip Ernst, Kari Lock Morgan, and Donald Rubin), Biometrika, 105, 745-752, 2018.
• Rate-optimal perturbation bounds for singular subspaces with applications to high-Dimensional statistics (with Tony Cai), The Annals of Statistics, 46, 60-89, 2018.
• Estimation of Markov chain via rank-constrained likelihood (with Mengdi Wang and Xudong Li), International Conference on Machine Learning (ICML), PMLR 80:3033-3042, 2018.
• Structured matrix completion with applications in genomic data integration (with Tianxi Cai and Tony Cai), Journal of American Statistical Association, 111, 621-633, 2016. [R package]
• Regression Analysis for Microbiome Compositional Data (with Pixu Shi and Hongzhe Li), The Annals of Applied Statistics, 10, 1019-1040, 2016. [Matlab package]
• Instrumental variables estimation with some invalid instruments and its application to Mendelian randomization (with Hyunseung Kang, Tony Cai and Dylan Small), Journal of American Statistical Association, 111, 132-144, 2016. [R Package]
• Minimax rate-optimal estimation of high-dimensional covariance matrices with incomplete data (with Tony Cai), Journal of Multivariate Analysis, 150, 55-74, 2016.
• Inference for high-dimensional differential correlation matrices (with Tony Cai), Journal of Multivariate Analysis, 143, 107-126, 2016.
• ROP: matrix recovery via rank-one projections (with Tony Cai), The Annals of Statistics, 43, 102-138, 2015.
• Sparse representation of a polytope and recovery of sparse signals and low-rank matrices (with Tony Cai), IEEE Transactions on Information Theory, 60, 122-132, 2014.
• Sharp RIP bound for sparse signal and low-rank matrix recovery (with Tony Cai), Applied and Computational Harmonic Analysis, 35, 74-93, 2013.
• Compressed sensing and affine rank minimization under restricted isometry (with Tony Cai), IEEE Transactions on Signal Processing, 61, 3279-3290, 2013.

Collaborative Research

• Ventriculomegaly and postoperative intraventricular blood predict cerebrospinal fluid diversion following posterior fossa tumor resection (Park, C., Liu, B., Harward, S., Zhang, A. R. et al.), Journal of Neurosurgery: Pediatrics, to appear.
• Denoising Atomic Resolution 4D Scanning Transmission Electron Microscopy Data with Tensor Singular Value Decomposition (with Chenyu Zhang, Rungang Han, and Paul Voyles), Ultramicroscopy, 219, 113123, 2020.
• LTMG: a novel statistical modeling of transcriptional expression states in single-cell RNA-Seq data (Wan, C. et al.) Nucleic Acids Research, 2019.

Other Manuscripts

• High-dimensional statistical inference: from vector to matrix
  PhD Thesis, 2015.
• Methods to calculate the upper bound of Gini coefficient based on grouped data and the result for China (with Pixu Shi)
  preprint of Institute of Mathematics, Peking University, 2010-20.