2 research outputs found
Feature Robust Optimal Transport for High-dimensional Data
Optimal transport is a machine learning problem with applications including
distribution comparison, feature selection, and generative adversarial
networks. In this paper, we propose feature-robust optimal transport (FROT) for
high-dimensional data, which solves high-dimensional OT problems using feature
selection to avoid the curse of dimensionality. Specifically, we find a
transport plan with discriminative features. To this end, we formulate the FROT
problem as a min--max optimization problem. We then propose a convex
formulation of the FROT problem and solve it using a Frank--Wolfe-based
optimization algorithm, whereby the subproblem can be efficiently solved using
the Sinkhorn algorithm. Since FROT finds the transport plan from selected
features, it is robust to noise features. To show the effectiveness of FROT, we
propose using the FROT algorithm for the layer selection problem in deep neural
networks for semantic correspondence. By conducting synthetic and benchmark
experiments, we demonstrate that the proposed method can find a strong
correspondence by determining important layers. We show that the FROT algorithm
achieves state-of-the-art performance in real-world semantic correspondence
datasets
Scalable Nearest Neighbor Search for Optimal Transport
The Optimal Transport (a.k.a. Wasserstein) distance is an increasingly
popular similarity measure for rich data domains, such as images or text
documents. This raises the necessity for fast nearest neighbor search
algorithms according to this distance, which poses a substantial computational
bottleneck on massive datasets. In this work we introduce Flowtree, a fast and
accurate approximation algorithm for the Wasserstein- distance. We formally
analyze its approximation factor and running time. We perform extensive
experimental evaluation of nearest neighbor search algorithms in the
distance on real-world dataset. Our results show that compared to previous
state of the art, Flowtree achieves up to times faster running time.Comment: ICML 202