  Given a database, computing the fraction of rows that contain a query itemset
or determining whether this fraction is above some threshold are fundamental
operations in data mining. A uniform sample of rows is a good sketch of the
database in the sense that all sufficiently frequent itemsets and their
approximate frequencies are recoverable from the sample, and the sketch size is
independent of the number of rows in the original database. For many seemingly
similar problems there are better sketching algorithms than uniform sampling.
In this paper we show that for itemset frequency sketching this is not the
case. That is, we prove that there exist classes of databases for which uniform
sampling is a space optimal sketch for approximate itemset frequency analysis,
up to constant or iterated-logarithmic factors.
