HyperLogLog is a classic probabilistic algorithm that approximates the number of distinct elements in a massive dataset using only one pass over the data. In the original article, Flajolet, Fusy, Gandouet, and Meunier (2007) provided a sharp analysis of the expectation and variance of the output, utilizing techniques such as poissonization and Mellin transform. This article revisits the analysis of HyperLogLog from a more probabilistic viewpoint, allowing the establishment of exponential deviation inequalities for the HyperLogLog estimator. The methods are elementary, yet the estimates are non-asymptotic and completely explicit.
Blogger's Review: The significance of the HyperLogLog algorithm in big data scenarios cannot be overstated. Its efficiency and accuracy make it a staple in data analysis. This paper's probabilistic reanalysis enhances our understanding of the algorithm's performance, particularly in terms of estimation accuracy. With clear non-asymptotic estimates, researchers can better control error bounds, providing stronger theoretical support for practical applications.