  Computing space-efficient summary, or \textit{a.k.a. sketches}, of large
data, is a central problem in the streaming algorithm. Such sketches are used
to answer \textit{post-hoc} queries in several data analytics tasks. The
algorithm for computing sketches typically requires to be fast, accurate, and
space-efficient. A fundamental problem in the streaming algorithm framework is
that of computing the frequency moments of data streams. The frequency moments
of a sequence containing $f_i$ elements of type $i$, are the numbers
$\mathbf{F}_k=\sum_{i=1}^n {f_i}^k,$ where $i\in [n]$. This is also called as
$\ell_k$ norm of the frequency vector $(f_1, f_2, \ldots f_n).$ Another
important problem is to compute the similarity between two data streams by
computing the inner product of the corresponding frequency vectors. The seminal
work of Alon, Matias, and Szegedy~\cite{AMS}, \textit{a.k.a. Tug-of-war} (or
AMS) sketch gives a randomized sublinear space (and linear time) algorithm for
computing the frequency moments, and the inner product between two frequency
vectors corresponding to the data streams. However, the variance of these
estimates typically tends to be large. In this work, we focus on minimizing the
variance of these estimates. We use the techniques from the classical
Control-Variate method~\cite{Lavenberg} which is primarily known for variance
reduction in Monte-Carlo simulations, and as a result, we are able to obtain
significant variance reduction, at the cost of a little computational overhead.
We present a theoretical analysis of our proposal and complement it with
supporting experiments on synthetic as well as real-world datasets.
