  Recently, Bessa et al. (PODS 2023) showed that sketches based on coordinated
weighted sampling theoretically and empirically outperform popular linear
sketching methods like Johnson-Lindentrauss projection and CountSketch for the
ubiquitous problem of inner product estimation. We further develop this finding
by introducing and analyzing two alternative sampling-based methods. In
contrast to the computationally expensive algorithm in Bessa et al., our
methods run in linear time (to compute the sketch) and perform better in
practice, significantly beating linear sketching on a variety of tasks. For
example, they provide state-of-the-art results for estimating the correlation
between columns in unjoined tables, a problem that we show how to reduce to
inner product estimation in a black-box way. While based on known sampling
techniques (threshold and priority sampling) we introduce significant new
theoretical analysis to prove approximation guarantees for our methods.
