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

TL;DR

This paper introduces algorithms based on optimal transport to match patterns in data, specifically applied to understanding micro-RNA regulation in Huntington's disease models, demonstrating effectiveness through simulations and real data.

Contribution

The paper develops novel algorithms combining optimal transport and affine transformations for pattern matching in biological data, with applications to omics data analysis.

Findings

Algorithms successfully match data patterns in simulations.

Application to real omics data reveals biologically relevant patterns.

Methods outperform baseline approaches in pattern detection.

Abstract

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.