[Sds-seminars] S&DS In-Person Seminar, Oscar Leong, 03/01 @ 4pm-5pm, "The Power and Limitations of Convexity in Data Science"

[elizavette.torres at yale.edu]

 <https://statistics.yale.edu/>     <https://statistics.yale.edu/>
Department of Statistics and Data Science  

In-Person seminars will be held at Mason Lab 211, 9 Hillhouse Avenue with
the option of virtual participation (
<https://yale.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx?folderID=f
8b73c34-a27b-42a7-a073-af2d00f90ffa>
https://yale.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx?folderID=f8
b73c34-a27b-42a7-a073-af2d00f90ffa)

 <https://0.0.0.10/> 3:30pm -   Pre-talk meet and greet teatime - Dana
House, 24 Hillhouse Avenue 


Oscar Leong, Caltech


Date: Wednesday, March 01, 2023

Time: 4:00PM to 5:00PM

Location: Mason Lab, Rm. 211
<http://maps.google.com/?q=9+Hillhouse+Ave%2C+New+Haven%2C+CT%2C+06511%2C+us
> see map 

9 Hillhouse Ave

New Haven, CT 06511

 <https://www.oscarleong.com/> Website

 

Title: The Power and Limitations of Convexity in Data Science

 

Information and Abstract: 

Optimization is a fundamental pillar of data science. Traditionally, the art
and challenge in optimization lay primarily in problem formulation to ensure
desirable properties such as convexity. In the context of contemporary data
science, however, optimization is practiced differently, with scalable local
search methods applied to nonconvex objectives being the dominant paradigm
in high-dimensional problems. This has brought a number of foundational
mathematical challenges at the interface between optimization and data
science pertaining to the dichotomy between convexity and nonconvexity.

In this talk, I will discuss some of my work addressing these challenges in
regularization, a technique to encourage structure in solutions to
statistical estimation and inverse problems. Even setting aside
computational considerations, we currently lack a systematic understanding
from a modeling perspective of what types of geometries should be preferred
in a regularizer for a given data source. In particular, given a data
distribution, what is the optimal regularizer for such data and what are the
properties that govern whether it is amenable to convex regularization?
Using ideas from star geometry, Brunn-Minkowski theory, and variational
analysis, I show that we can characterize the optimal regularizer for a
given distribution and establish conditions under which this optimal
regularizer is convex. Moreover, I describe results establishing the
robustness of our approach, such as convergence of optimal regularizers with
increasing sample size and statistical learning guarantees with applications
to several classes of regularizers of interest.

 

For more details and upcoming events visit our website at
<http://statistics.yale.edu/> http://statistics.yale.edu/

 

Department of Statistics and Data Science

Yale University
24 Hillhouse Avenue
New Haven, CT 06511

t 203.432.0666
f 203.432.0633

 

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