skip to main content

Search for: All records

Creators/Authors contains: "Li, Xudong"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. Free, publicly-accessible full text available April 1, 2023
  2. Modeling unknown systems from data is a precursor of system optimization and sequential decision making. In this paper, we focus on learning a Markov model from a single trajectory of states. Suppose that the transition model has a small rank despite having a large state space, meaning that the system admits a low-dimensional latent structure. We show that one can estimate the full transition model accurately using a trajectory of length that is proportional to the total number of states. We propose two maximum-likelihood estimation methods: a convex approach with nuclear norm regularization and a nonconvex approach with rank constraint. We explicitly derive the statistical rates of both estimators in terms of the Kullback-Leiber divergence and the [Formula: see text] error and also establish a minimax lower bound to assess the tightness of these rates. For computing the nonconvex estimator, we develop a novel DC (difference of convex function) programming algorithm that starts with the convex M-estimator and then successively refines the solution till convergence. Empirical experiments demonstrate consistent superiority of the nonconvex estimator over the convex one.
  3. High-temperature poling eliminates light-scattering domain walls in a relaxor ferroelectric.
    Free, publicly-accessible full text available April 22, 2023