  Optimal transport aligns samples across distributions by minimizing the
transportation cost between them, e.g., the geometric distances. Yet, it
ignores coherence structure in the data such as clusters, does not handle
outliers well, and cannot integrate new data points. To address these
drawbacks, we propose InfoOT, an information-theoretic extension of optimal
transport that maximizes the mutual information between domains while
minimizing geometric distances. The resulting objective can still be formulated
as a (generalized) optimal transport problem, and can be efficiently solved by
projected gradient descent. This formulation yields a new projection method
that is robust to outliers and generalizes to unseen samples. Empirically,
InfoOT improves the quality of alignments across benchmarks in domain
adaptation, cross-domain retrieval, and single-cell alignment.
