Statistics Colloquium Series


Monday, March 28, 2022, 12:00pm to 1:00pm


Science Center, Room 316

Our next event for the Statistics Department Colloquium Series is scheduled for this Monday, March 28th from 12:00 – 1:00pm (ET) and will be an in person presentation in room 316 of the Science Center. The speaker is Andrew Nobel who is a Robert Paul Ziff Distinguished Professor in the Department of Statistics and Operations Research at University of North Carolina.

Title : Stationary Optimal Transport with Applications to Graph Alignment

Abstract : Optimal transport seeks to find couplings of two given distributions with minimum expected cost. This talk considers the setting in which the distributions of interest are stationary stochastic processes, and the cost function depends only on a finite number of coordinates. In this setting, I will argue that it is appropriate, and desirable, to restrict attention to stationary couplings, also known as joinings.

The first part of the talk will address estimation of optimal joinings from observations of two ergodic processes. I will then consider optimal transport for Markov chains via transition couplings, beginning with fast computation based on techniques from reinforcement learning. As an illustration, I will show how optimal joinings of Markov chains can be used to effectively compare two weighted graphs with potentially different node sets. This approach yields interpretable alignments of nodes and edges, has a desirable edge-preserving property, and implicitly account for graph factors when these exist.

Bio: Andrew Nobel is the Robert Paul Ziff Distinguished Professor of Statistics and Operations Research at UNC Chapel Hill. His research interests include optimal transport, dynamical systems, and statistical genomics. His research encompasses mathematical foundations and methodological development, as well as real-world applications. His work has addressed an array of problems, including uniform ergodic theorems for VC-classes, matrix reconstruction in Gaussian noise, analysis, and implementation of biclustering procedures for large average submatrices, community detection in weighted networks, and analysis of joint and individual variation in multi-view genomic data. Nobel is a fellow of the IMS, and is currently an Associate Editor at JRSS-B.