Feature Robust Optimal Transport for High-dimensional Data-猫眼课题宝

DOI：

10.1007/978-3-031-26419-1_18

发表时间：

2020-05

期刊：

ArXiv

影响因子：

通讯作者：

中科院分区：

其他

文献类型：

作者：

Mathis Petrovich;Chao Liang;Yanbin Liu;Yao-Hung Hubert Tsai;Linchao Zhu;Yi Yang;R. Salakhutdinov;M. Yamada

最佳运输是一个机器学习问题，其应用包括分布比较，特征选择和生成对抗网络。在本文中，我们提出了高维数据的特征鲁棒最优传输（FROT），它解决了高维OT问题，使用特征选择，以避免维数灾难。具体来说，我们找到了一个具有歧视性特征的运输计划。为此，我们制定的FROT问题作为一个最小最大优化问题。然后，我们提出了一个凸公式的FROT问题，并解决它使用基于Frank-Wolfe的优化算法，从而可以有效地解决子问题使用Sinkhorn算法。由于FROT从选定的特征中找到运输计划，因此它对噪声特征具有鲁棒性。为了证明FROT的有效性，我们建议使用FROT算法来解决深层神经网络中的层选择问题，以实现语义对应。通过进行合成和基准实验，我们证明，该方法可以找到一个强对应，通过确定重要层。我们表明，FROT算法在现实世界的语义对应数据集上实现了最先进的性能。代码可在https://github.com/Mathux/FROT上找到。

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. Code can be found at https://github.com/Mathux/FROT.

Feature Robust Optimal Transport for High-dimensional Data

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