Date: Tuesday, January 12, 2021 at 11:00 am

Link: https://bluejeans.com/6622130444

Title: Inverse Problems and Machine Learning

Abstract: 

The fields of inverse problems and machine learning have a lot in common. In fact, many of the algorithms and problems in each of these fields can be analyzed and developed from the perspective of the other. In this talk I give an overview of some of my research at the intersection of these fields. In the first part I will discuss the asymptotic consistency of a graphical semi-supervised learning algorithm. Using ideas from theory of inverse problems and spectral analysis of elliptic operators to develop a deeper understanding of how and why graphical algorithms work. In the second part of the talk, I will present an algorithm for data-driven solution of Bayesian inverse problems by combining tools from machine learning, such as generative adversarial networks, with ideas in measure transport. This approach leads to a model agnostic method for conditional sampling and in turn the solution of inverse problems.

Bio: 

I am a Senior postdoctoral scholar in the Department of Computing and Mathematical Sciences (CMS) at California Institute of Technology sponsored by Profs. Andrew Stuartand Houman Owhaid. Prior to that I was a von Karman instructor in CMS. I received my Ph.D. in Applied and Computational Mathematics from Simon Fraser University under supervision of Profs. Nilima Nigam  and John Stockie. Broadly speaking, my research lies at the interface of probability, statistics, and applied mathematics with a particular focus on data science and uncertainty quantification. I also work on several applications in science and engineering such as atmospheric dispersion modelling, medical imaging, opinion formation in social networks and dynamics of power networks.