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Given a lossy-compressed representation, or sketch, of data with values in aset of symbols, the frequency recovery problem considers the estimation of theempirical frequency of a new data point. Recent studies have applied Bayesiannonparametrics (BNPs) to develop learning-augmented versions of the popularcount-min sketch (CMS) recovery algorithm. In this paper, we present a novelBNP approach to frequency recovery, which is not built from the CMS but stillrelies on a sketch obtained by random hashing. Assuming data to be modeled asrandom samples from an unknown discrete distribution, which is endowed with aPoisson-Kingman (PK) prior, we provide the posterior distribution of theempirical frequency of a symbol, given the sketch. Estimates are then obtainedas mean functionals. An application of our result is presented for theDirichlet process (DP) and Pitman-Yor process (PYP) priors, and in particular:i) we characterize the DP prior as the sole PK prior featuring a property ofsufficiency with respect to the sketch, leading to a simple posteriordistribution; ii) we identify a large sample regime under which the PYP priorleads to a simple approximation of the posterior distribution. Then, we developour BNP approach to a "traits" formulation of the frequency recovery problem,not yet studied in the CMS literature, in which data belong to more than onesymbol (trait), and exhibit nonnegative integer levels of associations witheach trait. In particular, by modeling data as random samples from ageneralized Indian buffet process, we provide the posterior distribution of theempirical frequency level of a trait, given the sketch. This result is thenapplied under the assumption of a Poisson and Bernoulli distribution for thelevels of associations, leading to a simple posterior distribution and a simpleapproximation of the posterior distribution, respectively.

Random measure priors in Bayesian frequency recovery from sketches