Accelerating jackknife resampling for the Canonical Polyadic Decomposition

TL;DR

This paper introduces an extension of the Concurrent ALS (CALS) method to accelerate jackknife resampling in Canonical Polyadic tensor decomposition, significantly reducing computational costs while maintaining accuracy.

Contribution

It presents a novel CALS extension that efficiently handles jackknife resampling, enabling faster uncertainty estimation in tensor decompositions.

Findings

CALS extension reduces jackknife computation time by several times.

The method incurs only a small increase in floating point operations.

Numerical experiments confirm substantial speedups on synthetic and real datasets.

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.