Generative Entropic Neural Optimal Transport To Map Within and Across Space

Dominik Klein, Théo Uscidda, Fabian J Theis, marco cuturi

Primary Area: general machine learning (i.e., none of the above)

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.

Keywords: optimal transport, single-cell biology

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.

Abstract:

Learning measure-to-measure mappings is a crucial task in machine learning, fea-
tured prominently in generative modeling. Recent years have witnessed a surge of
techniques that draw inspiration from optimal transport (OT) theory. Combined
with neural network models, these methods collectively known as Neural OT use
optimal transport as an inductive bias: such mappings should be optimal w.r.t. a
given cost function, in the sense that they are able to move points in a thrifty way,
within (by minimizing displacements) or across spaces (by being isometric). This
principle, while intuitive, is often confronted with several practical challenges that
require adapting the OT toolbox: cost functions other than the squared-Euclidean
cost can be challenging to handle, the deterministic formulation of Monge maps
leaves little flexibility, mapping across incomparable spaces raises multiple chal-
lenges, while the mass conservation constraint inherent to OT can provide too
much credit to outliers. While each of these mismatches between practice and
theory has been addressed independently in various works, we propose in this
work an elegant framework to unify them, called generative entropic neural op-
timal transport (GENOT). GENOT can accommodate any cost function; handles
randomness using conditional generative models; can map points across incompa-
rable spaces, and can be used as an unbalanced solver. We evaluate our approach
through experiments conducted on various synthetic datasets and demonstrate its
practicality in single-cell biology. In this domain, GENOT proves to be valu-
able for tasks such as modeling cell development, predicting cellular responses to
drugs, and translating between different data modalities of cells.

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.

Submission Number: 7888