We present several algorithms designed to learn a pattern of correspondence between two data sets in situations where it is desirable to match elements that exhibit a relationship belonging to a known parametric model. In the motivating case study, the challenge is to better understand micro-RNA regulation in the striatum of Huntington's disease model mice. The algorithms unfold in two stages. First, an optimal transport plan P and an optimal affine transformation are learned, using the Sinkhorn-Knopp algorithm and a mini-batch gradient descent. Second, P is exploited to derive either several co-clusters or several sets of matched elements. A simulation study illustrates how the algorithms work and perform. The real data application further illustrates their applicability and interest.
@article{arxiv.2107.11192,
title = {Optimal transport-based machine learning to match specific patterns: application to the detection of molecular regulation patterns in omics data},
author = {Thi Thanh Yen Nguyen and Warith Harchaoui and Lucile Mégret and Cloe Mendoza and Olivier Bouaziz and Christian Neri and Antoine Chambaz},
journal= {arXiv preprint arXiv:2107.11192},
year = {2023}
}