  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 \beta-potential term associated with the
so-called $\beta$-divergence, which was developed in robust statistics. Our
theoretical analysis reveals that the $\beta$-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
