I am an assistant professor in the Department of Statistics, University of Illinois, with affiliation to the Department of Electrical and Computer Engineering. I am broadly interested in statistical inference, information theory, and high-dimensional statistics/probability. Many problems in these fields boil down to optimizing high-dimensional random functions or functions of multi-dimensional distributions. Information theory has deep connections to high-dimensional probability, and recent breakthroughs have been achieved by exploiting the rich interplay between the two. Functional inequalities, Markov semigroups, hypercontractivity, optimal transport, convex geometry, and auxiliary random variables have proven to be powerful tools for settling important open questions and unlocking new insights. Researchers have made significant progress in understanding the fundamental limits of communication, cryptography, statistics, and machine learning in high-dimensional settings.
I also taught and conducted research on statistical physics techniques for high-dimensional problems (such as distributional limits of lasso and the free energy of tensor models), and the applications in variable selection and PCA. The lecture notes linked below provide tutorials on common methods for proofs of distributional limits (replica, cavity, AMP, and convex geometry) on basic toy example settings. Feedback and comments are highly appreciated!
e-mail: jingbol@illinois.edu
Address:
Room 228, Computing Applications Building, 605 E Springfield Ave, Champaign, IL 61820
For a list of my publications and courses I have taught, please see my CV