Exploiting the Structure: Stochastic Gradient Methods Using Raw Clusters
This work addresses the problem of handling large datasets efficiently for machine learning practitioners, though it appears incremental as it builds on existing methods with clustering enhancements.
The paper tackles empirical risk minimization by exploiting data clustering structure to develop faster algorithms, resulting in ClusterACDM and ClusterSVRG outperforming classical methods like ACDM and SVRG.
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 \emph{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.