IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Efficient Search Engine Measurements

We address the problem of externally measuring aggregate functions over documents indexed by search engines, like corpus size, index freshness, and density of duplicates in the corpus. The recently proposed estimators for such quantities [5, 8] are biased due to inaccurate approximation of the so called “document degrees”. In addition, the estimators in [5] are quite costly, due to their reliance on rejection sampling. We present new estimators that are able to overcome the bias introduced by approximate degrees. Our estimators are based on a careful implementation of an approximate importance sampling procedure. Comprehensive theoretical and empirical analysis of the estimators demonstrates that they have essentially no bias even in situations where document degrees are poorly approximated. By avoiding the costly rejection sampling approach, our new importance sampling estimators are significantly more efficient than the estimators proposed in [5]. Furthermore, building on an idea from [8], we discuss Rao-Blackwellization as a generic method for reducing variance in search engine estimators. We show that Rao-Blackwellizing our estimators results in performance improvements, while not compromising accuracy.