Subsampled online matrix factorization with convergence guarantees

Abstract : We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains more than 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low complexity per iteration and reasonable memory footprint. In contrast to previous online matrix factorization methods, our approach relies on low-dimensional statistics from past iterates to control the extra variance introduced by subsampling. We present a convergence analysis that guarantees us to reach a stationary point of the problem. Large speed-ups can be obtained compared to previous online algorithms that do not perform subsampling, thanks to the feature redundancy that often exists in high-dimensional settings.
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Submitted on : Wednesday, November 30, 2016 - 7:54:22 PM
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Arthur Mensch, Julien Mairal, Gaël Varoquaux, Bertrand Thirion. Subsampled online matrix factorization with convergence guarantees. NIPS Workshop on Optimization for Machine Learning, Dec 2016, Barcelone, Spain. ⟨hal-01405058⟩

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