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We present several algorithms designed to learn a pattern of correspondencebetween two data sets in situations where it is desirable to match elementsthat exhibit a relationship belonging to a known parametric model. In themotivating case study, the challenge is to better understand micro-RNAregulation in the striatum of Huntington's disease model mice. The algorithmsunfold in two stages. First, an optimal transport plan P and an optimal affinetransformation are learned, using the Sinkhorn-Knopp algorithm and a mini-batchgradient descent. Second, P is exploited to derive either several co-clustersor several sets of matched elements. A simulation study illustrates how thealgorithms work and perform. The real data application further illustratestheir applicability and interest.

Optimal transport-based machine learning to match specific patterns: application to the detection of molecular regulation patterns in omics data