October 25, 2024

List of Speakers

1. Genevera Allen, Columbia University

2. Zoraida F. Rico, Columbia University

Genevera Allen: 

Joint Semi-Symmetric Tensor PCA for Integrating Multi-modal Populations of Networks

Abstract: Multi-modal populations of networks arise in many scenarios including in large-scale multi-modal neuroimaging studies that capture both functional and structural neuroimaging data for thousands of subjects. A major research question in such studies is how functional and structural brain connectivity are related and how they vary across the population. We develop a novel PCA-type framework for integrating multi-modal undirected networks measured on many subjects. Specifically, we arrange these networks as semi-symmetric tensors, where each tensor slice is a symmetric matrix representing a network from an individual subject. We then propose a novel Joint, Integrative Semi-Symmetric Tensor PCA (JisstPCA) model, associated with an efficient iterative algorithm, for jointly finding low-rank representations of two or more networks across the same population of subjects. We establish one-step statistical convergence of our separate low-rank network factors as well as the shared population factors to the true factors, with finite sample statistical error bounds. Through simulation studies and a real data example for integrating multi-subject functional and structural brain connectivity, we illustrate the advantages of our method for finding joint low-rank structures in multi-modal populations of networks.

Zoraida F. Rico:

Title: Fine bounds on covariance estimation

Abstract: We present an estimator of the covariance matrix of a random d-dimensional vector from an i.i.d. finite sample. We assume the data have relatively heavy tails and allow for an adversary to modify an arbitrary fraction of the sample. Given this, we show that the covariance can be estimated with the same high-probability error rates that the sample covariance matrix achieves in the case of Gaussian data. This work is joint with Roberto I. Oliveira (IMPA) and has been accepted for publication in the Annals of Statistics.

Directions

The Columbia Statistics Department is located on Amsterdam Ave between 121st and 122nd Street. The nearest MTA stations are the 1 train 125th Street Station and the A train 125th Street station.