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# Robust computation of optimal transport by $β$-potential regularization

*Proceedings of The 14th Asian Conference on Machine Learning*, PMLR 189:770-785, 2023.

#### Abstract

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.