  We consider the problem of computing differentially private approximate
histograms and heavy hitters in a stream of elements. In the non-private
setting, this is often done using the sketch of Misra and Gries [Science of
Computer Programming, 1982]. Chan, Li, Shi, and Xu [PETS 2012] describe a
differentially private version of the Misra-Gries sketch, but the amount of
noise it adds can be large and scales linearly with the size of the sketch: the
more accurate the sketch is, the more noise this approach has to add. We
present a better mechanism for releasing Misra-Gries sketch under
$(\varepsilon,\delta)$-differential privacy. It adds noise with magnitude
independent of the size of the sketch size, in fact, the maximum error coming
from the noise is the same as the best known in the private non-streaming
setting, up to a constant factor. Our mechanism is simple and likely to be
practical. We also give a simple post-processing step of the Misra-Gries sketch
that does not increase the worst-case error guarantee. It is sufficient to add
noise to this new sketch with less than twice the magnitude of the
non-streaming setting. This improves on the previous result for
$\varepsilon$-differential privacy where the noise scales linearly to the size
of the sketch.
