Seminar on Data Science and Applied Mathematics - Randomized tensor-network algorithms for random data in high-dimensions

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.

Short-Bio: Yuehaw Khoo is an assistant Professor at the department of statistics, University of Chicago. He works on computational mathematics with applications in high dimensional PDE, optimization and imaging problems. Previously, he did his postdoctoral study at Stanford University with Lexing Ying and graduate study at Princeton University with Amit Singer.