The tensor network representation of high order cumulant and algorithm for their calculation

In this paper we introduce a novel algorithm of calculating arbitrary order cumulants of multidimensional data. Since the n order cumulant can be presented in the form of an n-dimensional tensor, the algorithm is presented using the tensor network notation. The presented algorithm exploits the super–symmetry of cumulant and moment tensors. We show, that proposed algorithm highly decreases the computational complexity of cumulants calculation, compared to the naïve algorithm.