Unbiased Ranking Evaluation on a Budget

Abstract

We address the problem of assessing the quality of a rank-ing system (e.g., search engine, recommender system, review ranker) given a fixed budget for collecting expert judgments. In particular, we propose a method that selects which items to judge in order to optimize the accuracy of the quality es-timate. Our method is not only efficient, but also provides estimates that are unbiased — unlike common approaches that tend to underestimate performance or that have a bias against new systems that are evaluated re-using previous relevance scores [1]. Our method is based on the insight that we can write many common performance measures as expectations, and then use Monte Carlo techniques, such as importance sampling, to estimate these expectations [1]. We compare against the traditional approach of ranking evaluation under budget constraints that is employed in the pooling method used in TREC [8]. Instead of judging all queries to their full depths, only the top k (e.g., k = 100) documents for each query are judged until the budget is exhausted. While for small document collections it is rea-sonable to assume that all relevant documents are within the top k documents, this working hypothesis is less valid for larger collections [3]. More complicated approaches in-clude stratified sampling or greedy sample selection [11, 2], but usually result in algorithms that are difficult to apply for practitioners. Somewhat related to our method is the scenario in which one wants to re-use interaction logs of a system for evaluation [6, 7] or data from logged interleaving experiments [4]. Our contributions are as follows. First, we show how to get an unbiased estimator for Discounted Cumulative Gain (DCG) [5] using importance sampling. Second, we out-line a simple proposal for selecting the sampling distribu-tion. Lastly, we compare our method to two traditional approaches and show that it is vastly superior in terms of bias and accuracy