论文标题
有效的强大最佳运输，并应用于多标签分类
Efficient Robust Optimal Transport with Application to Multi-Label Classification
论文作者
论文摘要
最佳传输（OT）是一种强大的几何工具，用于比较两个分布，并已在各种机器学习应用中使用。在这项工作中，我们提出了一种新颖的OT公式，该公式在学习两个分布之间的运输计划时考虑了特征相关性。我们通过在OT成本函数中通过对称正极半明确的Mahalanobis指标对特征功能关系进行建模。对于指标上的一类正规化器，我们表明可以通过利用问题结构来大大简化优化策略。对于高维数据，我们还提出了Mahalanobis度量的合适的低维模型。总体而言，我们将最终的优化问题视为非线性OT问题，我们使用Frank-Wolfe算法解决了该问题。关于歧视性学习环境（例如TAG预测和多级分类）的经验结果说明了我们方法的良好表现。
Optimal transport (OT) is a powerful geometric tool for comparing two distributions and has been employed in various machine learning applications. In this work, we propose a novel OT formulation that takes feature correlations into account while learning the transport plan between two distributions. We model the feature-feature relationship via a symmetric positive semi-definite Mahalanobis metric in the OT cost function. For a certain class of regularizers on the metric, we show that the optimization strategy can be considerably simplified by exploiting the problem structure. For high-dimensional data, we additionally propose suitable low-dimensional modeling of the Mahalanobis metric. Overall, we view the resulting optimization problem as a non-linear OT problem, which we solve using the Frank-Wolfe algorithm. Empirical results on the discriminative learning setting, such as tag prediction and multi-class classification, illustrate the good performance of our approach.
