Analytical confidence intervals for the number of different objects in data streams
This work addresses the statistical analysis of popular big data stream algorithms, which has often been handled heuristically, offering a more rigorous foundation for practitioners in data streaming.
This paper tackles the problem of estimating the number of distinct elements in data streams using Flajolet-Martin algorithms, providing analytical confidence intervals based on Chernoff bounds and showing connections to special functions and extreme value theory. The result includes testing on real data and Monte Carlo simulations to validate the approach.
This paper develops a new mathematical-statistical approach to analyze a class of Flajolet-Martin algorithms (FMa), and provides analytical confidence intervals for the number F0 of distinct elements in a stream, based on Chernoff bounds. The class of FMa has reached a significant popularity in bigdata stream learning, and the attention of the literature has mainly been based on algorithmic aspects, basically complexity optimality, while the statistical analysis of these class of algorithms has been often faced heuristically. The analysis provided here shows deep connections with mathematical special functions and with extreme value theory. The latter connection may help in explaining heuristic considerations, while the first opens many numerical issues, faced at the end of the present paper. Finally, the algorithms are tested on an anonymized real data stream and MonteCarlo simulations are provided to support our analytical choice in this context.