A New Algorithm for Compressed Counting with Applications in Shannon Entropy Estimation in Dynamic Data

In this paper, we propose a new accurate algorithm for Compressed Counting, whose sample complexity is only O (1/v2) for v-additive Shannon entropy estimation. The constant factor for this bound is merely about 6. In addition, we prove that our algorithm achieves an upper bound of the Fisher information and in fact it is close to 100% statistically optimal. An empirical study is conducted to verify the accuracy of our algorithm.