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

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.