  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
statistics. 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 asymptotic variance.
Given fixed sampling budgets for different statistics, we derive the optimal
weights to combine the individual estimators; given fixed total budget, we show
that a greedy allocation towards the most efficient statistics 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
statistics. We show that our two-stage framework is a generalization of 1)
randomly choosing a statistics 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.
