Bias Correction in a Small Sample from Big Data

This paper discusses the bias problem when estimating the population size of big data such as online social networks (OSN) using uniform random sampling and simple random walk. Unlike the traditional estimation problem where the sample size is not very small relative to the data size, in big data, a small sample relative to the data size is already very large and costly to obtain. We point out that when small samples are used, there is a bias that is no longer negligible. This paper shows analytically that the relative bias can be approximated by the reciprocal of the number of collisions; thereby, a bias correction estimator is introduced. The result is further supported by both simulation studies and the real Twitter network that contains 41.7 million nodes.