Abstract

In this paper, we introduce a novel algorithm for calculating arbitrary order cumulants of multidimensional data. Since the $d{th}$ order cumulant can be presented in the form of a $d$-dimensional tensor, the algorithm is presented using tensor operations. The algorithm provided in the paper takes advantage of supersymmetry of cumulant and moment tensors. We show that the proposed algorithm considerably reduces the computational complexity and the computational memory requirement of cumulant calculation as compared with existing algorithms. For the sizes of interest, the reduction is of the order of $d!$ compared to the naive algorithm.

Keywords

  1. high-order cumulants
  2. nonnormally distributed data
  3. numerical algorithms

MSC codes

  1. 65Y05
  2. 15A69
  3. 65C60

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Information & Authors

Information

Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: A1590 - A1610
ISSN (online): 1095-7197

History

Submitted: 26 September 2017
Accepted: 9 April 2018
Published online: 5 June 2018

Keywords

  1. high-order cumulants
  2. nonnormally distributed data
  3. numerical algorithms

MSC codes

  1. 65Y05
  2. 15A69
  3. 65C60

Authors

Affiliations

Funding Information

Narodowe Centrum Nauki https://doi.org/10.13039/501100004281 : 2014/15/B/ST6/05204

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