Sequential Bayesian Estimation in State-Space Models using Tensor Trains

Abstract

Numerous real-world applications require the estimation, forecasting, and control of dynamic systems using incomplete and indirect observations. These problems can be formulated as state-space models, in which the primary challenge lies in simultaneously learning the states and parameters from observed data. In this talk, we present novel tensor-based sequential Bayesian learning methods that jointly estimate parameters and states. Our methods facilitate manageable error analysis and potentially mitigate the particle degeneracy encountered in traditional particle-based approaches. Additionally, our framework naturally incorporates conditional transport mappings, enabling filtering, smoothing, and parameter estimation within a unified algorithmic structure.

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.