High Probability Frequency Moment Sketches

We consider the problem of sketching the $p$-th frequency moment of a vector, $p>2$, with multiplicative error at most $1\pm ε$ and \emph{with high confidence} $1-δ$. Despite the long sequence of work on this problem, tight bounds on this quantity are only known for constant $δ$. While one can obtain an upper bound with error probability $δ$ by repeating a sketching algorithm with constant error probability $O(\log(1/δ))$ times in parallel, and taking the median of the outputs, we show this is a...