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

Wenjie Zheng 1 Aurélien Bellet 2 Patrick Gallinari 1
2 MAGNET - Machine Learning in Information Networks
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : 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.
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Submitted on : Wednesday, November 14, 2018 - 7:16:05 PM
Last modification on : Friday, January 21, 2022 - 3:20:38 AM
Long-term archiving on: : Friday, February 15, 2019 - 4:42:42 PM


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Wenjie Zheng, Aurélien Bellet, Patrick Gallinari. A Distributed Frank-Wolfe Framework for Learning Low-Rank Matrices with the Trace Norm. Machine Learning, Springer Verlag, 2018, ⟨10.1007/s10994-018-5713-5⟩. ⟨hal-01922994⟩



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