January 25, 2022

12:00 pm / 1:00 pm

ZOOM MEETING LINK:  https://wse.zoom.us/j/99304114570

?Stochastic and ConvexGeometry for the Analysis of Complex Data?

ElizaO’Reilly PhD     

Postdoctoral Fellow    

Computingand Mathematical Sciences                              

California Institute of Technology

Abstract:  Manymodern problems in data science aimto efficiently and accurately extractimportant features and make predictions from high dimensional and large datasets. While there are many empirically successful methods to achieve thesegoals, large gaps between theory andpractice remain. A geometricviewpoint is often useful to address these challenges as it provides a unifyingperspective of structure in data, complexity of statistical models, andtractability of computational methods.As a consequence, an understanding ofproblem geometry leads both to new insights on existing methods as well as newmodels and algorithms that address drawbacks in existing methodology.

In this talk, Iwill presentrecent progress on two problems where the relevant model can beviewed as the projection of a lifted formulation with a simple stochastic orconvex geometric description. In particular, I will first describe how thetheory of stationary random tessellations in stochastic geometry can addresscomputational and theoretical challenges of random decision forests withnon-axis-aligned splits. Second, I will present a new approach to convexregression that returns non-polyhedral convex estimators compatible withsemidefinite programming. These works open a number of future researchdirections in the mathematics of data science.

Biography:  Eliza O’Reilly is aPostdoctoral Scholar Fellowship Trainee in Computing and Mathematical Sciencesand NSF Postdoctoral Fellow at the California Institute of Technology sponsoredby Profs. VenkatChandrasekaranand Joel Tropp. Eliza received herPhD in Mathematics in August 2019 from the University of Texas at Austin where shewas fortunate to be advised by Prof. François Baccelli.

Eliza’sresearch interests lie broadly in the mathematics of data science. Herwork lies at the intersection of stochastic and convex geometry, highdimensional probability, and stochastic processes.