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 Journal of Scientific Computing
Start PageA1590
Other NumbersarXiv:1701.05420
Słowa kluczoweHigh order cumulants, non-normally distributed data, numerical algorithms

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.

Refereed DesignationRefereed