7 citations · 8 across the 8 of their papers we have counts for
9 papers
Quantitative Stability of the Shadow for Wasserstein Projections and Sample Complexity
Jakwang Kim
In this paper, we study the stability of the shadow, a projection of a measure onto the set of couplings with respect to the Wasserstein distance. The shadow was introduced by \cit…
Extension of coupling via the Projection of Optimal Transport
Jakwang Kim, Young-Heon Kim, Chan Park
In many statistical settings, two types of data are available: coupled data, which preserve the joint structure among variables but are limited in size due to cost or privacy const…
Stability of Wasserstein projections in convex order via metric extrapolation
Jakwang Kim, Young-Heon Kim, Andrea Natale
We build on recent work linking backward and forward W2-projections in convex order with the recently introduced metric extrapolation problem to derive new quantitative stability e…
Robust Estimation in metric spaces: Achieving Exponential Concentration with a Fréchet Median
Jakwang Kim, Jiyoung Park, Anirban Bhattacharya
There is growing interest in developing statistical estimators that achieve exponential concentration around a population target even when the data distribution has heavier than ex…
Optimal sequencing depth for single-cell RNA-sequencing in Wasserstein space
Jakwang Kim, Sharvaj Kubal, Geoffrey Schiebinger
How many samples should one collect for an empirical distribution to be as close as possible to the true population? This question is not trivial in the context of single-cell RNA-…
Statistical inference of convex order by Wasserstein projection
Jakwang Kim, Young-Heon Kim, Yuanlong Ruan +1
Ranking distributions according to a stochastic order has wide applications in diverse areas. Although stochastic dominance has received much attention, convex order, particularly…
An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classification
Nicolas Garcia Trillos, Matt Jacobs, Jakwang Kim +1
Despite the success of deep learning-based algorithms, it is widely known that neural networks may fail to be robust. A popular paradigm to enforce robustness is adversarial traini…
On the existence of solutions to adversarial training in multiclass classification
Nicolas Garcia Trillos, Matt Jacobs, Jakwang Kim
We study three models of the problem of adversarial training in multiclass classification designed to construct robust classifiers against adversarial perturbations of data in the…
The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classification
Nicolas Garcia Trillos, Matt Jacobs, Jakwang Kim
We study a family of adversarial multiclass classification problems and provide equivalent reformulations in terms of: 1) a family of generalized barycenter problems introduced in…