General Information
| Student: | Shivesh Mehrotra |
|---|---|
| School: | Yale University |
| E-mail: | shivesh (dot) mehrotra (@) yale (dot) edu |
| Project: | Statistical Inference and Automatic Differentiation of Iterative Algorithms |
| Mentor: | Pierre Bellec, Department of Statistics, Rutgers University |
Project Description
The goal of the project is to explore possible applications of automatic differentiation to help with the construction of confidence intervals and other statistical goals. Automatic differentiation is a powerful numerical tool to compute gradients functions, with no computational overhead compared to evaluating the function itself. It has found numerous applications in recent years, for instance it is the basis of modern deep learning implementations. Statistical inference in high dimensions aim to construct confidence intervals for unknown parameters, e.g., to quantify with high confidence the effect of a given human gene for a medical outcome of interest. Recent advances allow to construct such confidence intervals using the gradients of certain ideal functions of the observed data; these ideal functions are typically approximated by iterative algorithms. One possible research direction is to explore, numerically, the behavior of automatic differentiation when applied to these iterative algorithms: how do the computed gradients behave through the iterations, how well do they approximate the gradients of the ideal functions of interest, do confidence intervals built using these gradients yield valid statistical inference.
Weekly Log
Week 1: Understanding the LASSO and ISTA
We introduce the LASSO and ISTA and outline our goals for the project.
Read MoreAdditional Information
- My Mentor:
- Kai:
Acknowledgements
I would like to thank my mentor Pierre for being extraordinarily helpful and responsive throughout the program. I'd also like to thank Kai Tan for helping me understand concepts and being a wonderful teacher. Lastly I'd like to thank Max Ranis for being a mentor and guide throughout my education. Without Max I may have never pursued statistics and I'm thankful I've been influenced by him. This research is supported by NSF Grant CCF-1852215.