TY - JOUR

T1 - Accelerating jackknife resampling for the Canonical Polyadic Decomposition

AU - Psarras, Christos

AU - Karlsson, Lars

AU - Bro, Rasmus

AU - Bientinesi, Paolo

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - cs.MS

KW - cs.NA

KW - math.NA

U2 - 10.3389/fams.2022.830270

DO - 10.3389/fams.2022.830270

M3 - Journal article

VL - 8

JO - Frontiers in Applied Mathematics and Statistics

JF - Frontiers in Applied Mathematics and Statistics

SN - 2297-4687

M1 - 830270

ER -