Supervised quantile normalization for low-rank matrix approximation

Marco Cuturi, Olivier Teboul, Jonathan Niles-Weed, Jean Philippe Vert

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Low rank matrix factorization is a fundamental building block in machine learning, used for instance to summarize gene expression profile data or word-document counts. To be robust to outliers and differences in scale across features, a matrix factorization step is usually preceded by ad-hoc feature normalization steps, such as tf-idf scaling or data whitening. We propose in this work to learn these normalization operators jointly with the factorization itself. More precisely, given a d × n matrix X of d features measured on n individuals, we propose to learn the parameters of quantile normalization operators that can operate row-wise on the values of X and/or of its factorization UV to improve the quality of the low-rank representation of X itself. This optimization is facilitated by the introduction of a new differentiable quantile normalization operator built using optimal transport, providing new results on top of existing work by (Cuturi et al. 2019). We demonstrate the applicability of these techniques on synthetic and genomics datasets.

Original languageEnglish (US)
Title of host publication37th International Conference on Machine Learning, ICML 2020
EditorsHal Daume, Aarti Singh
PublisherInternational Machine Learning Society (IMLS)
Number of pages11
ISBN (Electronic)9781713821120
StatePublished - 2020
Event37th International Conference on Machine Learning, ICML 2020 - Virtual, Online
Duration: Jul 13 2020Jul 18 2020

Publication series

Name37th International Conference on Machine Learning, ICML 2020


Conference37th International Conference on Machine Learning, ICML 2020
CityVirtual, Online

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Human-Computer Interaction
  • Software


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