For most of the current research in high-dimensional inference, it is assumed that the underlying observations are independent and/or the tails are light. I am establishing a framework and a systematic theory for high-dimensional inference under dependence, and developing necessary tools so that the dependence can be accounted for. In particular, I am working on model selection, covariance matrix estimation, regression, mean vector estimation, and multiple testing problems for data with dependence. On the probabilistic side, I am interested in deviation and concentration inequalities for dependent random variables which may not have exponential moments. I am also investigating the deep Gaussian approximation problem.
Last update: 04/20/16