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Time & Location*:
Wednesdays from 11am – 12pm in Hill 005
(*Some talks may be scheduled for different times or locations. Such details will be provided additionally.)

 

Organizers:
Narek Hovsepyan
nh507@math.rutgers.edu
Gokul Nair
gokul.nair@rutgers.edu
(For inquiries, e.g. to be added to the mailing list, please contact either one of the organizers.)

 

 

*27 January (Monday) at 4 – 5 pm in Hill 525
Gabriel Rioux, Cornell University
“Gromov-Wasserstein Alignment: Statistics and Computation.”
Abstract
Over the past decade, the statistical and computational properties of optimal transport (OT) have been systematically studied, driven, in part, to its broad applicability to data science. This program has culminated in an in depth understanding of the curse of dimensionality that OT distances suffer and spurred the development of computationally and statistically efficient proxies thereof via regularization. While OT distances enable a natural comparison between distributions on the same space, comparing datasets of different types (e.g., text and images) requires defining an ad hoc cost function which may not capture a meaningful correspondence between data points.
In this talk, I will survey the current statistical and computational landscape for Gromov-Wasserstein (GW) distances, a framework which enables comparing abstract metric measure spaces based on their intrinsic metric structure and, as such, have seen widespread use in applications including comparing datasets of different types. I will present the first limit laws obtained for empirical GW distances, both with and without regularization, and describe consistent resampling schemes. Additionally, I will introduce the first algorithms for computing regularized GW distance subject to formal convergence guarantees. I will conclude by highlighting a number of open questions and future directions in the study of GW distances.
Joint work with Ziv Goldfeld and Kengo Kato

 

*30 January (Thursday) at 10:45 – 11:45 am in Hill 705
Joint with Math and Data Seminar
Sangmin Park, Carnegie Mellon University
“PDEs, data science, and optimal transport.”
Abstract

In this talk I will present two works lying at the interface between PDEs, data science, and optimal transport.

The first part concerns the dissipative Hamiltonian structure of the Vlasov-Fokker-Planck equation (VFP). VFP describes the evolution of the probability density of the position and velocity of particles under the influence of external confinement, interaction, friction, and stochastic force. It is well-known that this equation can be formally seen as a dissipative Hamiltonian system in the Wasserstein space of probability measures. Moreover, this geometric structure has possible connections to the conjectured optimal convergence rates of underdamped Langevin Monte Carlo (ULMC), a sampling algorithm known to empirically outperform the (standard) Langevin Monte Carlo. This talk will focus on a time-discrete variational scheme for VFP which we introduce to more rigorously understand the geometric structure.

The second part, based on a joint work with Dejan Slepcev, concerns the sliced Wasserstein distance. The sliced Wasserstein metric compares probability measures by taking averages of the Wasserstein distances between projections of the measures to lines. The distance has found a range of applications in statistics and machine learning, as it is easier to approximate and compute in high dimensions than the (classical) Wasserstein distance. We will focus on our characterization of the disparate behavior of the sliced Wasserstein distance near absolutely continuous and discrete measures. We will explain the connection between this characterization and the maximum mean discrepancies (MMDs) which helps understand the behavior of the distance in high dimensions. If time permits, we will also discuss a refined result on the sample complexity of the metric and the instability of sliced Wasserstein gradient flows.

 

*6 February (Thursday) at 2 – 3 pm in TBD
Tom Hagstrom, Southern Methodist University
“TBA.”
Abstract

TBA

 

19 February
Pierre Amenoagbadji, Columbia University
“TBA.”
Abstract

TBA

 

12 March
Mahadevan Ganesh, Colorado School of Mines
“TBA.“
Abstract

TBA.

 

9 April
Amir Sagiv, NJIT
“TBA.”
Abstract

TBA.