On the Sample Complexity of Compressed Counting

The problem of “scaling up for high dimensional data and high speed data streams” is among the “ten challenging problems in data mining research”[36]. This paper is devoted to estimating entropy of data streams. Mining data streams[19, 4, 1, 29] in (e.g.,) 100 TB scale databases has become an important area of research, e.g., [10, 1], as network data can easily reach that scale[36]. Search engines are a typical source of data streams[4]. Consider the Turnstile stream model[29]. The input stream at = (it, It), it ∈ [1, D] arriving sequentially describes the underlying signal A, meaning