which provides a similar trade-off and also needs less space than the original method, could be used alternatively.

Sometimes not only the number of distinct elements but also a sample of them is needed in order to allow later filtering according to some predicate and estimating the cardinalities of corresponding subsets. In this case the k-minimum values algorithm [@Beyer2007; @Cohen2007] is the method of choice. It needs more space than the algorithm, but also allows set manipulations like construction of intersections, relative complements, or unions [@Dasgupta2015]. The latter operation is the only one that is natively supported by sketches. A sketch that represents the set operation result is not always needed. One approach to estimate the corresponding result cardinality directly is based on the inclusion-exclusion principle, which however can lead to large errors, especially if the result is small compared to the input set sizes [@Dasgupta2015]. Therefore, it was proposed to combine sketches with minwise hashing [@Pascoe2013; @Cohen2016], which improves the estimation error, even though at the expense of significant more space consumption. It was recently pointed out without special focus on sketches, that the application of the method to the joint likelihood function of two probabilistic data structures leads 