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[1712.07495] A Distributed Frank-Wolfe Framework for Learning Low-Rank Matrices...

 2 years ago
source link: https://arxiv.org/abs/1712.07495
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[Submitted on 20 Dec 2017 (v1), last revised 11 May 2018 (this version, v2)]

A Distributed Frank-Wolfe Framework for Learning Low-Rank Matrices with the Trace Norm

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We consider the problem of learning a high-dimensional but low-rank matrix from a large-scale dataset distributed over several machines, where low-rankness is enforced by a convex trace norm constraint. We propose DFW-Trace, a distributed Frank-Wolfe algorithm which leverages the low-rank structure of its updates to achieve efficiency in time, memory and communication usage. The step at the heart of DFW-Trace is solved approximately using a distributed version of the power method. We provide a theoretical analysis of the convergence of DFW-Trace, showing that we can ensure sublinear convergence in expectation to an optimal solution with few power iterations per epoch. We implement DFW-Trace in the Apache Spark distributed programming framework and validate the usefulness of our approach on synthetic and real data, including the ImageNet dataset with high-dimensional features extracted from a deep neural network.

Subjects: Distributed, Parallel, and Cluster Computing (cs.DC); Machine Learning (cs.LG); Machine Learning (stat.ML) DOI: 10.1007/s10994-018-5713-5 Cite as: arXiv:1712.07495 [cs.DC]   (or arXiv:1712.07495v2 [cs.DC] for this version)

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