Accelerating Jackknife Resampling for the Canonical Polyadic Decomposition

Frontiers in Applied Mathematics and Statistics, vol. 8

Abstract

The Canonical Polyadic (CP) tensor decomposition is frequently used as a model in applications in a variety of different fields. Using jackknife resampling to estimate parameter uncertainties is often desirable but results in an increase of the already high computational cost. Upon observation that the resampled tensors, though different, are nearly identical, we show that it is possible to extend the recently proposed Concurrent ALS (CALS) technique to a jackknife resampling scenario. This extension gives access to the computational efficiency advantage of CALS for the price of a modest increase (typically a few percent) in the number of floating point operations. Numerical experiments on both synthetic and real-world datasets demonstrate that the new workflow based on a CALS extension can be several times faster than a straightforward workflow where the jackknife submodels are processed individually.

Authors 4

1. Christos Psarras Aachen International Research Training Group Aachen Institute for Advanced Study in Computational Engineering Science (AICES) Department of Computer Science

   Aachen Institute for Advanced Study in Computational Engineering Science · RWTH Aachen University

   Affiliation as printed

   International Research Training Group, Aachen Institute for Advanced Study in Computational Engineering Science (AICES), Department of Computer Science, RWTH Aachen University, Aachen, Germany

2. Lars Karlsson

   Umeå University

   Affiliation as printed

   High-Performance and Automatic Computing Group, Department of Computing Science, Umeå University, Umeå, Sweden

3. Rasmus Bro

   University of Copenhagen

   Affiliation as printed

   Department of Food Science, Institute for Fødevarevidenskab, University of Copenhagen, Copenhagen, Denmark

4. Paolo Bientinesi corresponding

   Umeå University

   Affiliation as printed

   High-Performance and Automatic Computing Group, Department of Computing Science, Umeå University, Umeå, Sweden