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Unbiased Comparative Evaluation of Ranking Functions
Eliciting relevance judgments for ranking evaluation is labor-intensive and
costly, motivating careful selection of which documents to judge. Unlike
traditional approaches that make this selection deterministically,
probabilistic sampling has shown intriguing promise since it enables the design
of estimators that are provably unbiased even when reusing data with missing
judgments. In this paper, we first unify and extend these sampling approaches
by viewing the evaluation problem as a Monte Carlo estimation task that applies
to a large number of common IR metrics. Drawing on the theoretical clarity that
this view offers, we tackle three practical evaluation scenarios: comparing two
systems, comparing systems against a baseline, and ranking systems. For
each scenario, we derive an estimator and a variance-optimizing sampling
distribution while retaining the strengths of sampling-based evaluation,
including unbiasedness, reusability despite missing data, and ease of use in
practice. In addition to the theoretical contribution, we empirically evaluate
our methods against previously used sampling heuristics and find that they
generally cut the number of required relevance judgments at least in half.Comment: Under review; 10 page
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