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Exploiting the Structure: Stochastic Gradient Methods Using Raw Clusters
Zeyuan Allen-Zhu · Yang Yuan · Karthik Sridharan

Wed Dec 07 09:00 AM -- 12:30 PM (PST) @ Area 5+6+7+8 #11

The amount of data available in the world is growing faster than our ability to deal with it. However, if we take advantage of the internal structure, data may become much smaller for machine learning purposes. In this paper we focus on one of the fundamental machine learning tasks, empirical risk minimization (ERM), and provide faster algorithms with the help from the clustering structure of the data. We introduce a simple notion of raw clustering that can be efficiently computed from the data, and propose two algorithms based on clustering information. Our accelerated algorithm ClusterACDM is built on a novel Haar transformation applied to the dual space of the ERM problem, and our variance-reduction based algorithm ClusterSVRG introduces a new gradient estimator using clustering. Our algorithms outperform their classical counterparts ACDM and SVRG respectively.

Author Information

Zeyuan Allen-Zhu (Princeton University)
Yang Yuan (Cornell University)
Karthik Sridharan (University of Pennsylvania)

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