Abstract: In this talk, I will first introduce the concept of gradient flow as a continuous version of gradient descent, and how gradient flow solves the variational problems. With this background, I will introduce Langevin and Stein Variational Gradient Descent (SVGD) algorithms, which are particle methods for sampling from an unknown distribution, and can be obtained as discretizations of certain gradient flows on the space of probability measures. Next, I will introduce our proposal of Regularized Stein Variational Gradient Flow, which interpolates between the Stein Variational Gradient Flow and the Wasserstein Gradient Flow, and present its theoretical properties along with preliminary numerical evidence of its improved performance over SVGD.

Joint work with Ye He (UC Davis), Krishnakumar Balasubramanian (UC Davis), and Jianfeng Lu (Duke)