Welcome to the Geometry, Statistics and Optimization lab led by professors Lizhen Lin and Dong Quan Nguyen!

The goal of our lab is to study broad statistical and optimization problems arising in data science. We aim to advance fundamental theory, algorithms and computational tools for statistics and optimization. One of our key insights are to employ geometric and topological tools for statistics inference and optimizations. For example, we have been utilizing topology and geometry for network analysis and big data analysis. Our research can be summarized in the following four general categories.

We gratefully acknowledge the funding support from NSF DMS program, NSF IIS program, Army's Research Office and DARPA. 

Geometry and Statistics

Geometry and Statistics

Geometry (e.g., differential geometry, Riemannian geometry, Algebraic geometry) is inherent in many areas of statistics with geometry is either unknown or to be learnt, which should be incorporated or utilized for inference.
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Optimization

Optimization

Theory and algorithms are being developed for general areas of optimizations such as optimization on manifolds, non-convex optimization and integer optimization. Interface between statistics and optimization is explored.
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Network Analysis

Network Analysis

Algebraic and geometric tools are utilized for network analysis leveraging insights from algebraic topology and geometry. Bayesian modeling strategies are also considered for network models. Multiplex and dynamic networks are primary objects of study.
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Big Data Analysis

Big Data Analysis

The focus is on (1) learning lower-dimensional structure of big data; (2) estimation and hypothesis testing of covariance matrices of high-dimensional data; (3) developing dividing and conquering strategy of big data analysis.
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News and Announcements

NIPS 2018

Several NIPS submissions. Wish us good luck this year!

July 2018 DARPA meeting

The PIs presented a poster at a DARPA meeting on Topological modelings of networks.