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Found 5 papers, 4 papers with code
An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classification
Recent works have developed a connection between AT in the multiclass classification setting and multimarginal optimal transport (MOT), unlocking a new set of tools to study this problem.
Estimation of entropy-regularized optimal transport maps between non-compactly supported measures
In the case that the target measure is compactly supported or strongly log-concave, we show that for a recently proposed in-sample estimator, the expected squared $L^2$-error decays at least as fast as $O(n^{-1/3})$ where $n$ is the sample size.
On Rank Energy Statistics via Optimal Transport: Continuity, Convergence, and Change Point Detection
This paper considers the use of recently proposed optimal transport-based multivariate test statistics, namely rank energy and its variant the soft rank energy derived from entropically regularized optimal transport, for the unsupervised nonparametric change point detection (CPD) problem.
Measure Estimation in the Barycentric Coding Model
Our first main result leverages the Riemannian geometry of Wasserstein-2 space to provide a procedure for recovering the barycentric coordinates as the solution to a quadratic optimization problem assuming access to the true reference measures.
Multivariate rank via entropic optimal transport: sample efficiency and generative modeling
We leverage this result to demonstrate fast convergence of sample sRE and sRMMD to their population version making them useful for high-dimensional GoF testing.
