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The estimation of coverage probabilities, and in particular of the missingmass, is a classical statistical problem with applications in numerousscientific fields. In this paper, we study this problem in relation torandomized data compression, or sketching. This is a novel but practicallyrelevant perspective, and it refers to situations in which coverageprobabilities must be estimated based on a compressed and imperfect summary, orsketch, of the true data, because neither the full data nor the empiricalfrequencies of distinct symbols can be observed directly. Our contribution is aBayesian nonparametric methodology to estimate coverage probabilities from datasketched through random hashing, which also solves the challenging problems ofrecovering the numbers of distinct counts in the true data and of distinctcounts with a specified empirical frequency of interest. The proposed Bayesianestimators are shown to be easily applicable to large-scale analyses incombination with a Dirichlet process prior, although they involve some opencomputational challenges under the more general Pitman-Yor process prior. Theempirical effectiveness of our methodology is demonstrated through numericalexperiments and applications to real data sets of Covid DNA sequences, classicEnglish literature, and IP addresses.

Bayesian nonparametric estimation of coverage probabilities and distinct counts from sketched data