论文标题
通过$β$ - 电位正则化对最佳运输的强大计算
Robust computation of optimal transport by $β$-potential regularization
论文作者
论文摘要
最佳传输（OT）已成为机器学习字段中广泛使用的工具，以测量概率分布之间的差异。例如，OT是一种流行的损失函数，可量化经验分布与参数模型之间的差异。最近，通常使用熵罚款和著名的sndhorn算法以计算有效的方式近似原始ot。但是，由于sindhorn算法运行与Kullback-Leibler Divergence相关的投影，因此它通常很容易受到异常值的影响。为了克服这个问题，我们提出与与所谓的$β$ divergence相关的β-电位项正规化的，该项是在强大的统计中开发的。我们的理论分析表明，$β$ - 电势可以防止质量运输到异常值。我们在实验上证明，使用算法计算的传输矩阵即使在存在异常值的情况下，也有助于稳健地估算概率分布。此外，我们提出的方法可以成功地检测到受污染数据集的异常值
Optimal transport (OT) has become a widely used tool in the machine learning field to measure the discrepancy between probability distributions. For instance, OT is a popular loss function that quantifies the discrepancy between an empirical distribution and a parametric model. Recently, an entropic penalty term and the celebrated Sinkhorn algorithm have been commonly used to approximate the original OT in a computationally efficient way. However, since the Sinkhorn algorithm runs a projection associated with the Kullback-Leibler divergence, it is often vulnerable to outliers. To overcome this problem, we propose regularizing OT with the β-potential term associated with the so-called $β$-divergence, which was developed in robust statistics. Our theoretical analysis reveals that the $β$-potential can prevent the mass from being transported to outliers. We experimentally demonstrate that the transport matrix computed with our algorithm helps estimate a probability distribution robustly even in the presence of outliers. In addition, our proposed method can successfully detect outliers from a contaminated dataset
