LANS Informal Seminar: Vivak Patel

Seminar Title: Static Parameter Estimation using Kalman Filtering and Proximal Operators
Speaker: Vivak Patel, PhD Student, University of Chicago

Date/Time: 2015-12-02 15:00
Location: Bldg 240 rm 4301

Description:
In the data sciences, the estimation of stationary parameters under resource constraints has led to renewed interest in proximal optimization algorithms. In this talk, I present one such proximal optimization algorithm which leverages the principles of Kalman Filtering.

First, I will overview how classical statistics formulates parameter estimation as a variational problem, and how classical optimization techniques fare in comparison to proximal methods in minimizing the variational problem. I will then give a statistical interpretation of proximal methods, and show how this naturally leads to using the Kalman Filter. Then, I will review current Kalman Filtering theory, and how it is limited for static parameter estimation. Using Kalman’s original insights, I will give a different intuition for why the filter succeeds. This leads to our proximal method, Kalman-based Stochastic Gradient Descent (kSGD). I will then give convergence results for kSGD and support them with numerical evidence using a large data set. If time permits, I will also present some connections between kSGD and solving linear systems, and between kSGD and shrinkage estimation