Big Data is Low Rank

Abstract

Abstract: Matrices of low rank are pervasive in big data, appearing in recommender systems, movie preferences, topic models, medical records, and genomics. While there is a vast literature on how to exploit low rank structure in these datasets, there is less attention on explaining why low rank structure appears in the first place. In this talk, we explain the abundance of low rank matrices in big data by proving that certain latent variable models associated to piecewise analytic functions are of log-rank. Any large matrix from such a latent variable model can be approximated, up to a small error, by a low rank matrix. Armed with this theorem, we show how to use a low rank modeling framework to exploit low rank structure even for datasets that are not numeric, with applications in the social sciences, medicine, and automated machine learning.

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