Efficient computation of higher order cumulant tensors

TytułEfficient computation of higher order cumulant tensors
Publication TypeJournal Article
Rok publikacji2018
AutorzyDomino K, Gawron P, Pawela Ł
JournalSIAM J. SCI. COMPUT.
Volume40
Issue3
Start PageA1590
PaginationA1610
Other NumbersarXiv:1701.05420
Słowa kluczoweHigh order cumulants, non-normally distributed data, numerical algorithms
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 an d-dimensional tensor, the
algorithm is presented using tensor operations. The algorithm provided in the
paper takes advantage of super-symmetry 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.

URLhttps://epubs.siam.org/doi/abs/10.1137/17M1149365
DOI10.1137/17M1149365
Refereed DesignationRefereed

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