Statistics Seminar - Fall 2024

For questions about the seminar schedule, please contact Chong Jin.

September 12

Dr. Sheng Xu, Princeton University

Maximum likelihood for high-noise group orbit estimation and cryo-EM

Motivated by applications to single-particle cryo-electron microscopy (cryo-EM), we study a problem of group orbit estimation where samples of an unknown signal are observed under uniform random rotations from a rotational group. In high-noise regime, we describe a stratification of the Fisher information eigenvalues according to transcendence degrees in the algebra of group invariants. We relate the critical points of the log-likelihood optimization landscape to those of a sequence of moment matching problems. Some examples including a simplified model of cryo-EM will be discussed

Homepage: https://sx67.github.io/

November 14

Dr. Kangjie Zhou, Columbia University 

Dynamic Factor Analysis of High-dimensional Recurrent Events

Recurrent event time data arise in many studies, including biomedicine, public health, marketing, and social media analysis. High-dimensional recurrent event data involving large numbers of event types and observations become prevalent with the advances in information technology. This paper proposes a semiparametric dynamic factor model for the dimension reduction and prediction of high-dimensional recurrent event data. The proposed model imposes a low-dimensional structure on the mean intensity functions of the event types while allowing for dependencies. A nearly rate-optimal smoothing-based estimator is proposed. An information criterion that consistently selects the number of factors is also developed. Simulation studies demonstrate the effectiveness of these inference tools. The proposed method is applied to grocery shopping data, for which an interpretable factor structure is obtained. Based on joint work with Fangyi Chen, Yunxiao Chen and Zhiliang Ying.

Homepage: https://kangjie287.github.io/