ﻻ يوجد ملخص باللغة العربية
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.
We introduce a new method of performing high dimensional discriminant analysis, which we call multiDA. We achieve this by constructing a hybrid model that seamlessly integrates a multiclass diagonal discriminant analysis model and feature selection c
Missing data is a crucial issue when applying machine learning algorithms to real-world datasets. Starting from the simple assumption that two batches extracted randomly from the same dataset should share the same distribution, we leverage optimal tr
We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator mapping a Hi
Feature selection is an important tool to deal with high dimensional data. In unsupervised case, many popular algorithms aim at maintaining the structure of the original data. In this paper, we propose a simple and effective feature selection algorit
We introduce COT-GAN, an adversarial algorithm to train implicit generative models optimized for producing sequential data. The loss function of this algorithm is formulated using ideas from Causal Optimal Transport (COT), which combines classic opti