The count-min sketch data structure is used to estimate the frequencies of individual elements in a data stream. The authors note that the analysis of their data structure is simpler than other related data structures like the count sketch, technically because they're able to use Markov's inequality rather than Chebyshev's inequality, but conceptually because previous data structures are based on random projection models related to the Johnson-Lindenstrauss lemma and the tug-of-war sketch.
Has there been any work done in reframing the count-min sketch as some sort of random projection in the style of these previous data structures? Or has there been any work done showing that it's not possible to frame the data structure this way? Intuitively, I'd imagine there would be some technical difficulties involved in making this approach work because the count-min sketch is not an unbiased estimator and therefore isn't likely amenable to techniques showing that it works by embedding a higher-dimensional space inside a lower one with low distortion, but it would be interesting to see if there was a way of casting the analysis in this light.