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We study how to recover the frequency of a symbol in a large discrete dataset, using only a compressed representation, or sketch, of those data obtainedvia random hashing. This is a classical problem in computer science, withvarious algorithms available, such as the count-min sketch. However, thesealgorithms often assume that the data are fixed, leading to overly conservativeand potentially inaccurate estimates when dealing with randomly sampled data.In this paper, we consider the sketched data as a random sample from an unknowndistribution, and then we introduce novel estimators that improve upon existingapproaches. Our method combines Bayesian nonparametric and classical(frequentist) perspectives, addressing their unique limitations to provide aprincipled and practical solution. Additionally, we extend our method toaddress the related but distinct problem of cardinality recovery, whichconsists of estimating the total number of distinct objects in the data set. Wevalidate our method on synthetic and real data, comparing its performance tostate-of-the-art alternatives.

Frequency and cardinality recovery from sketched data: a novel approach bridging Bayesian and frequentist views