Stat Cafe - Abhishek Roy
The Symbiotic Relationship of Statistics and Optimization: Insights and Future
- Time: Wednesday 11/13/2024 from 11:30 AM to 12:30 PM
- Location: BLOC 411
- Food and drinks provided
Description
In this talk, I’ll explore the close relationship between statistics and optimization, illustrating how each field enhances the other in tackling complex data problems. The presentation will be divided into two parts. In the first part, | will talk about algorithms for Instrumental Variable Regression (IVaR) by viewing the problem as a Conditional Stochastic Optimization (CSO) problem. In the context of least-squares IVaR, our algorithms neither require matrix inversions nor mini-batches and provides a fully online approach for performing instrumental variable regression with streaming data. When the true model is linear, we derive rates of convergence in expectation, that are of order O(log T/T) and O(1/T™1-1) for any L > O, respectively under the availability of two-sample and one-sample oracles, where T is the number of iterations. Importantly, under the availability of the two-sample oracle, our procedure avoids explicitly modeling and estimating the relationship between the independent and the instrumental variables, demonstrating the benefit of the proposed approach over recent works based on reformulating the problem as minimax optimization problems. Numerical experiments are provided to corroborate the theoretical results. In the second part, | will talk about my future research directions. | will specifically focus on learning with dueling feedback, how does transformer learn and causal inference.