On updates of high order cumulant tensors
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High order cumulants carry information about statistics of non--normally distributed multivariate data. Such cumulants are utilised in extreme events analysis, small target detection or outliers detection. In this work we present a new algorithm,for updating high order cumulant tensors of random multivariate data, if new package of data is recorded. We show algebraically and numerically, that the proposed algorithm is faster than a naive cumulants recalculation algorithm. For investigated computer generated data our algorithm appears to be fasten than a naive one by 1-2 orders of magnitude. That update algorithm makes the online updates of multivariate data statistics much faster, and can be used for the data streaming analysis. Further we propose the map reduce algorithm of cumulants calculation, that is based on introduced cumulants updates algorithm. This map reduce algorithm can be used to collect statistics about multivariate confidential data that are held by many agents, without sharing those data.
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