arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2002.03229cs.LGstat.ML

Supervised Quantile Normalization for Low-rank Matrix Approximation

Google Research, Brain Team(谷歌研究院脑团队);New York University(纽约大学)

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

英文摘要:

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 \texttt{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 $d\times n$ 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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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