This Ph.D. level course will provide an overview of machine learning and its algorithmic paradigms, and explore recent topics on learning, inference, and decision-making with large data sets. Emphasis will be made on theoretical insights and algorithmic principles.
A statistical theory for N-of-1 experiments, where a unit serves as its own control and treatment in different time windows.
Blessings and curses of covariate shifts, directional convergece, and the connection to experimental design.
Motivated by robust dynamic resource allocation in operations research, we study the Online Learning to Transport (OLT) problem where the decision variable is a probability measure, an infinite-dimensional object. We draw connections between online learning, optimal transport, and partial differential equations through an insight called the minimal selection principle, originally studied in the Wasserstein gradient flow setting by Ambrosio et al. (2005).
This paper proposes a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification.
We study the detailed path-wise behavior of the discrete-time Langevin algorithm for non-convex Empirical Risk Minimization (ERM) through the lens of metastability, adopting some techniques from Berglund and Gentz (2003).
Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the sampling nature of the data. We introduce the moment-adjusted stochastic gradient descents, a new stochastic optimization method for statistical inference.