An Exploration of Optimization Algorithms for High Performance Tensor Completion

Shaden Smith, Jongsoo Park, George Karypis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Scopus citations

Abstract

Tensor completion is a powerful tool used to estimate or recover missing values in multi-way data. It has seen great success in domains such as product recommendation and healthcare. Tensor completion is most often accomplished via low-rank sparse tensor factorization, a computationally expensive non-convex optimization problem which has only recently been studied in the context of parallel computing. In this work, we study three optimization algorithms that have been successfully applied to tensor completion: Alternating least squares (ALS), stochastic gradient descent (SGD), and coordinate descent (CCD++). We explore opportunities for parallelism on shared- A nd distributed-memory systems and address challenges such as memory- A nd operation-efficiency, load balance, cache locality, and communication. Among our advancements are an SGD algorithm which combines stratification with asynchronous communication, an ALS algorithm rich in level-3 BLAS routines, and a communication-efficient CCD++ algorithm. We evaluate our optimizations on a variety of real datasets using a modern supercomputer and demonstrate speedups through 1024 cores. These improvements effectively reduce time-to-solution from hours to seconds on real-world datasets. We show that after our optimizations, ALS is advantageous on parallel systems of small-to-moderate scale, while both ALS and CCD++ will provide the lowest time-to-solution on large-scale distributed systems.

Original languageEnglish (US)
Title of host publicationProceedings of SC 2016
Subtitle of host publicationThe International Conference for High Performance Computing, Networking, Storage and Analysis
PublisherIEEE Computer Society
Pages359-371
Number of pages13
ISBN (Electronic)9781467388153
DOIs
StatePublished - Jul 2 2016
Event2016 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2016 - Salt Lake City, United States
Duration: Nov 13 2016Nov 18 2016

Publication series

NameInternational Conference for High Performance Computing, Networking, Storage and Analysis, SC
Volume0
ISSN (Print)2167-4329
ISSN (Electronic)2167-4337

Other

Other2016 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2016
Country/TerritoryUnited States
CitySalt Lake City
Period11/13/1611/18/16

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