Computational Mathematics and Statistics Seminar by Yuehaw Khoo: Randomized Tensor-Network Algorithms for Random Data in High-Dimensions

Speaker:

Yuehaw Khoo, assistant professor of statistics, University of Chicago

Title:

Randomized Tensor-Network Algorithms for Random Data in High-Dimensions

Abstract:

Tensor-network ansatz has long been employed to solve the high-dimensional Schrödinger equation, demonstrating linear complexity scaling with respect to dimensionality. Recently, this ansatz has found applications in various machine learning scenarios, including supervised learning and generative modeling, where the data originates from a random process. In this talk, we present a new perspective on randomized linear algebra, showcasing its usage in estimating a density as a tensor-network from i.i.d. samples of a distribution, without the curse of dimensionality, and without the use of optimization techniques. Moreover, we illustrate how this concept can combine the strengths of particle and tensor-network methods for solving high-dimensional PDEs, resulting in enhanced flexibility for both approaches.

Computational Mathematics and Statistics Seminar