Sampling online social networks via heterogeneous statistics

Most sampling techniques for online social networks (OSNs) are based on a particular sampling method on a single graph, which is referred to as a statistic. However, various realizing methods on different graphs could possibly be used in the same OSN, and they may lead to different sampling efficiencies, i.e., asymptotic variances. To utilize multiple statistics for accurate measurements, we formulate a mixture sampling problem, through which we construct a mixture unbiased estimator which minimizes the asymptotic variance. Given fixed sampling budgets for different statistics, we derive the optimal weights to combine the individual estimators; given a fixed total budget, we show that a greedy allocation towards the most efficient statistic is optimal. In practice, the sampling efficiencies of statistics can be quite different for various targets and are unknown before sampling. To solve this problem, we design a two-stage framework which adaptively spends a partial budget to test different statistics and allocates the remaining budget to the inferred best statistic. We show that our two-stage framework is a generalization of 1) randomly choosing a statistic and 2) evenly allocating the total budget among all available statistics, and our adaptive algorithm achieves higher efficiency than these benchmark strategies in theory and experiment.