Abstract
High-dimensional parameters arise naturally in many modern statistical problems — from regression with a large number of covariates to ranking models where the number of latent utilities grows with the size of the comparison graph. In this talk, I will present two recent works that address estimation and inference challenges in these high-dimensional and semiparametric settings.
The first part concerns online inference in high-dimensional generalized linear models with streaming data. We develop the Adaptive Debiased Lasso (ADL), which updates coefficient estimates and confidence intervals upon each new data arrival. The method features an adaptive stochastic gradient descent algorithm with a novel online debiasing procedure via Taylor approximation, achieving asymptotic normality with only O(p) space and time complexity instead of O(p²) in previous methods. In the second part, I will present a semiparametric model for ranking data whose underlying graph structure governs both the dimensionality of the problem and the difficulty of estimation. In the comparison hypergraph, each object's strength is modeled as the sum of a utility parameter and a nonparametric covariate effect approximated by a deep neural network. Non-asymptotic error bounds achieving minimax optimality for model components are established. The framework is demonstrated on an ATP tennis dataset that capturing nonlinear contextual effects in player performance.
Speaker Bio
Yuanhang Luo is currently a PhD student in the Department of Data Science and Artificial Intelligence at the Hong Kong Polytechnic University. He received his B.Sc. in Mathematics & Statistics from Hong Kong Baptist University. His research focuses on high-dimensional statistics, ranking and reinforcement learning.