Speaker: Tiangang Cui, Monash University
Time: 12:25-13:25 , Oct.22
Location: SIST 1C 101
Host: Prof. Qifeng Liao
Abstract:
Characterising intractable high-dimensional random variables is one of the fundamental challenges in stochastic computation. It has broad applications in statistical physics, machine learning, uncertainty quantification, econometrics, and beyond. The recent surge of transport maps offers a mathematical foundation and new insights for tackling this challenge.In this talk, we present a functional tensor-train (TT) based order-preserving construction of inverse Rosenblatt transport in high dimensions. It characterises intractable random variables via couplings with tractable reference random variables. By integrating our TT-based approach into a nested approximation framework inspired by deep neural networks, we are able to significantly expand its capability to random variables with complicated nonlinear interactions and concentrated density functions. We demonstrate the efficacy of the TT-based inverse Rosenblatt transport on a range of applications in statistical learning and uncertainty quantification, including parameter estimation for dynamical systems, PDE-constrained inverse problems, and Bayesian filtering.
Bio:
Tiangang Cui is a Senior Lecturer in the School of Mathematics at Monash University. He has previously held positions at Massachusetts Institute of Technology and the ExxonMobil Corporation. He has been worked on a wide range of topics on the intersection of data analytics and computational mathematics. His research interests include Bayesian inference,inverse problems, model reduction, and statistical learning.