Five papers are selected to represent our research before 2022, a complete list of publications is available at my Google Scholar page.
Acknowledgement. The research results presented on this page are supported by the grants NSF IIS 1546482-BIGDATA, NIH R01MH102339, NSF IIS1408910, NSF IIS1332109, NIH R01GM083084, NIH R01HG06841.
Combinatorial Inference for Graphical Models
Matey Neykov, Junwei Lu and Han Liu
The Annals of Statistics , Volume 47, Number 2 (2019), pp795-827.
Blurb. This paper proposes a new family of combinatorial inference problems which aim at testing the global structural properties of high dimenisonal graphical models. Our main contribution is to develop a unified theory to characterize the fundamental limits and efficient algorithms for a large family of combinatorial inference problems.
Property Testing in High Dimensional Ising models
Matey Neykov and Han Liu
The Annals of Statistics, Accepted. 2019.
Blurb. This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. In particular, we extended the theoretical results for combinatorial inference from Gaussian graphical models to Ising graphical models. Both information-theoretic upper and lower bounds are developed.
Pathwise Coordinate Optimization for Sparse Learning: Algorithm and Theory
Tuo Zhao, Han Liu, and Tong Zhang
The Annals of Statistics, Volume 46, Number 1 (2018), pp180-218.
Blurb. This paper develops a model-based statistical optimization theory to analyze the pathwise coordinate optimization algorithms.We solved an open problem on providing a matehmatical theory to justify the superior performance of the pathwise coordinate optimization strategies for convex/nonconvex sparse learning problems.
A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional Models
Yang Ning and Han Liu
The Annals of Statistics. Volume 45, Number 1 (2017), pp158-195.
Blurb. This paper considers both hypothesis tests and confidence regions for generic penalized M-estimators. Unlike most existing inferential methods which are tailored for individual models, our approach provides a general framework for high dimensional sparse inference (also called post-regularization inference).
High Dimensional Semiparametric Gaussian Copula Graphical Models
Han Liu, Fang Han, Ming Yuan, John Lafferty, and Larry Wasserman
The Annals of Statistics, Volume 40, Number 40 (2012), pp2293-2326.
Blurb. This paper proposes a regularized rank-based estimator (e.g., based on the Kendall's tau correlation coefficients) to fit the nonGaussian graphical model. We prove that the proposed procedure simultaneously achieves the optimal parametric rates of convergence for both graph recovery and parameter estimation.
