AMS Weekly Seminar | Associate Professor Krishna Balasubramanian

Location: Olin 305

When: May 2nd at 1:30 p.m.

Title: Geometry-aware algorithms for statistical data science

Abstract: Many problems arising in the realm of statistical data science could be naturally formulated as optimizing certain objectives over manifolds. Two specific examples include topology-preserving dimension reduction methods which are formulated as optimization problems over Riemannian manifolds (e.g., Stiefel manifold), and Bayesian sampling or variational inference problems which are formulated as optimization problems over the Bures-Wasserstein manifold. In this presentation, I will discuss two algorithmic advancements pertinent to the aforementioned problems.

The initial focus of the presentation will center on zeroth-order algorithms for Riemannian optimization within a stochastic fully-online framework. By leveraging a novel Riemannian moving-average stochastic gradient estimation technique, I will elucidate how to achieve optimal convergence guarantees to first-order stationary solutions, requiring just a single sample per iteration. The subsequent focus will shift to algorithms for solving the Gaussian variational inference problem over the Bures-Wasserstein manifold. I will outline the state-of-the-art convergence guarantees associated with our proposed algorithm, when the target density exhibits both log-smoothness and log-concavity, as well as the first convergence guarantee to first-order stationary solutions when the target density is solely log-smooth. Throughout the talk, fruitful interactions between the fields of geometry, probability and statistics for solving challenging optimization and sampling algorithms, ​which form the computational backbone of statistical data science, will be emphasized.

Bio: Krishna Balasubramanian is an Associate Professor in the Department of Statistics, University of California, Davis. He is also affiliated with the Graduate Group in Applied Mathematics, Graduate Program in Electrical and Computer Engineering, the Center for Data Science and Artificial Intelligence Research (CeDAR) and the TETRAPODS Institute of Data Science at UC Davis. He was a visiting scientist at the Simons Institute for the Theory of Computing, UC Berkeley in Fall 2021 and 2022. Previously, he completed his PhD in Computer Science from Georgia Institute of Technology, and was a postdoctoral researcher in the Department of Operations Research and Financial Engineering, Princeton University, and the Department of Statistics at UW-Madison. Krishna’s research interests include stochastic optimization and sampling, deep learning, nonparametric, geometric and topological Statistics. His research was/is supported by a Facebook PhD fellowship, and CeDAR and NSF grants. He serves as an associate editor for the Journal of Machine Learning Research and as a senior area chair for top machine learning conferences including the International Conference on Machine Learning (ICML), Advances in Neural Information Processing Systems (NeurIPS), International Conference on Learning Representations (ICLR), and Conference on Learning Theory (COLT).

Zoom link: https://wse.zoom.us/j/94601022340