InfoOT: Information Maximizing Optimal Transport

Ching-Yao Chuang, Stefanie Jegelka, David Alvarez-Melis

Keywords: Optimal Transport, Unsupervised Alignment, Domain Adaptation, Mutual Information

TL;DR: We present InfoOT, an information-theoretic extension of optimal transport that combines the geometry with the mutual information between domains.

Abstract: 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.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

Submission Guidelines: Yes

Please Choose The Closest Area That Your Submission Falls Into: General Machine Learning (ie none of the above)

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2210.03164/code)