Geodesics in fibered latent spaces: A geometric approach to learning correspondences between conditions

Autor:	Daouda, Tariq, Chhaibi, Reda, Tossou, Prudencio, Villani, Alexandra-Chloé
Rok vydání:	2020
Předmět:	Statistics - Machine Learning Computer Science - Machine Learning Mathematics - Differential Geometry Quantitative Biology - Genomics
Druh dokumentu:	Working Paper
Popis:	This work introduces a geometric framework and a novel network architecture for creating correspondences between samples of different conditions. Under this formalism, the latent space is a fiber bundle stratified into a base space encoding conditions, and a fiber space encoding the variations within conditions. Furthermore, this latent space is endowed with a natural pull-back metric. The correspondences between conditions are obtained by minimizing an energy functional, resulting in diffeomorphism flows between fibers. We illustrate this approach using MNIST and Olivetti and benchmark its performances on the task of batch correction, which is the problem of integrating multiple biological datasets together. Comment: 36 pages, many figures. v1: Preliminary version. v2: Minor ref fix. v3: Submitted version with enhanced presentation
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2005.07852 Zobrazit plný text záznamu View this record from Arxiv