Past Event: Oden Institute Seminar

From Matrix Interpolation to Tensorized High-Dimensional Random Variable Simulation with Applications to Bayesian Computation

Tiangang Cui, Senior Lecturer, University of Sydney

Abstract

Simulating intractable high-dimensional random variables is one of the fundamental challenges in stochastic computation. This task has broad applications in statistical physics, machine learning, uncertainty quantification, econometrics, and beyond. In this talk, we will present how to formulate such tasks as function approximation problems and solve them using tensor computation. We will also show how the tensor computation problem can be reduced to simple recursive matrix interpolations. As a result, we obtain algorithms with complexity linear in the problem dimension. We will demonstrate the efficiency and efficacy of our developed methods on a range of Bayesian computation problems, including parameter estimation for dynamical systems, PDE-constrained inverse problems, and rare event estimation.

Biography

Tiangang Cui is a Senior Lecturer in the School of Mathematics and Statistics at the University of Sydney. He earned his PhD in Engineering Science from the University of Auckland in 2011 and subsequently held a postdoctoral position at the Massachusetts Institute of Technology from 2012 to 2015. Before joining the University of Sydney in 2023, he served as a Lecturer and then Senior Lecturer at Monash University from 2016 to 2023. Dr. Cui's research focuses on computational mathematics for scientific machine learning and data science. He develops mathematically rigorous computational methods for statistical inverse problems, data assimilation, and uncertainty quantification. He has authored numerous publications in leading journals such as Foundations of Computational Mathematics, Bernoulli, Journal of Machine Learning Research, Journal of Computational Physics, etc.