Education and Training

• Postdoctoral Research Associate, Princeton University, 2013-2017
• PhD in Statistics, Purdue University, 2012
• MA in Mathematics, University of Hawaii, 2009
• MS in Mathematics, Sichuan University, 2006

Courses

• Stat412 and Stat437 and Stat115 and Stat435

Research Interests

• Analysis of non-Euclidean data (such as networks, shapes, images and tensors) (Active).
• Theoretical foundations of machine learning models (Active).
• Statistical inference on stochastic differential equations (including those driven by fractional Brownian motions) with applications in finance, biology and geology. (Dormant)
• Spectra of random matrices (including those of sample auto-correlation/auto-covariance matrices/adjacency matrices) with applications to inference on high-dimensional data. (Dormant)
• Simultaneous inference (including variable/model selection and multiple comparison) with applications in biology and pharmaceutical science. (Inactive)
• Latent variable models for high-dimensional data with applications in genomics and signal processing. (Inactive)

More on My Research and Me

Please read through my Research webpage (whose link is given below) and then contact me if you want to work with me.
• Research and CV ; R pacakge fdrDiscreteNull for my papers A and B and C
• Notes in Math and Notes in Statistics
• Miscellaneous and Some Open Problems

Working with Me

I strive to maintain high standards and high creativity in both my theoretical and applied research. As you might have already found out from my Research webpage, I am no longer doing research in high-dimensional simultaneous inference or high-dimensional sparse linear models. Instead, I am doing research on analysis of non-Euclidean data and on the theoretical foundation of machine learning models. Here are the tools that will be used in a theoretical project in any of the two active fields mentioned earlier:

• Core: Techniques in the books "Mathematical Statistics: Basic Ideas and Selected Topics, Volume I" by Kjell A. Doksum and Peter J. Bickel, "Real Analysis and Probability" by Robert B. Ash (or "Real Analysis and Probability" by R. M. Dudley), "Asymptotic Statistics" by Aad van der Vaart, "Real and Complex Analysis" by Walter Rudin, and "Introduction to Riemannian Manifolds" by John M. Lee, the last of which is needed for analysis of non-Euclidean data but not necessarily for the theoretical foundation of machine learning models.
• Supplementary: Techniques in "Measure Theory" by Paul Halmos, "Probability" by Albert N. Shiryaev, "A Course in Functional Analysis" by John B. Conway, "Riemannian Geometry" by Takashi Sakai, "A Comprehensive Introduction to Differential Geometry" by Michael Spivak, "Mathematical Foundations of Infinite-Dimensional Statistical Models" by Evarist Gine Masdeu and Richard Nickl, and “General Topology” by John L. Kelley. Familiarity with the basics of ordinary differential equations and partial differential equations, such as how to solve typical such equations and properties of their solutions.
• Default: Skills required by Statistics (or Math) GQE, and uni-variate and multi-variate calculus (e.g., "Differential and Integral Calculus, Volumes I and II" by Richard Courant) and linear algebra (e.g., "Lectures in Abstract Algebra, Volume II" by Nathan Jacobson). You also need to be good at R programming.

If you are interested in working with me on a theoretical project of my expertise, please schedule a meeting with me.

I may also have some applied projects that I may get through collaborations. However, eventually new methodologies (and their theories) will be proposed for their associated applied problems. Please note the difference between "a purely applied project" and "a methodological project": the former proposes no new methodology whereas the latter does. So, I will not work on purely applied projects since they do not have sufficient intellectual contributions. If you choose to work with me on an applied project as your PhD thesis research, we will need to develop new methodologies (but not neccesarily their accompanying theories), and together with me you will sharpen much your skills in probability and mathematical statistics beyond those offered by our courses.

Acknowledgements

I am very grateful in particular to Gerard Letac (Universite de Toulouse), Sanat K. Sarkar (Temple U), Armin Schwartzman (UCSD), Donald St. P. Richards (Penn State U), Hong-ming Yin (WSU), Yimin Xiao (Michigan State U), Persi Diaconis (Stanford U) and Wayne Smith (U of Hawaii) for advice and help on my research.