PhD Candidate Profile: Xintian Han
Who are our PhD students? Where do they come from, what are they studying now, and where do they hope to go in the future? Find out more about one of our PhD candidates, Xintian Han!
Xintian is from China, and obtained his B.S. degree in statistics from Peking University in 2017.
His current research interests focus on machine learning theory, methodologies and algorithms, especially on high dimensional problems, network models and deep learning. He is also interested in interdisciplinary research. He has done research on network sampling, and high dimensional statistics.
For network sampling, he develops a new model of respondent driven sampling without replacement and proves the asymptotic bounds of the variance of the estimator in this new model. He develops a simple linear time algorithm to sample a Poisson edge random dot product graph and extends this algorithm to sample simple graph and show that under certain settings this is an approximation to the Bernoulli edge random dot product graph. For high dimensional statistics, he shows the consistency of a new penalized weighted score function method to solve sparse Logistic regression problems.
He also proves the consistency of a new method to choose the tuning parameter based on the normal approximation of score function by Stein’s method. He introduces a general framework of de-biased estimators for convex penalty functions in high dimensional regression by inverting KKT condition. He proposes an “add-one-in” method to construct conﬁdence intervals for parameters in high dimensional problems, which uses LASSO to select the parameters and adds each one non-selected parameter into the selected set to build conﬁdence intervals by linear regression.