Robust computation of optimal transport by $β$-potential regularization
This work addresses robustness issues in optimal transport for machine learning applications, offering an incremental improvement over existing methods.
The paper tackles the vulnerability of Sinkhorn-based optimal transport to outliers by proposing a regularization with the β-potential term, and experimentally shows that this method robustly estimates probability distributions and detects outliers in contaminated datasets.
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