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Estimating retrieval effectiveness using rank distributions

In this paper, we consider the task of estimating query effectiveness, i.e., assessment of the retrieval system performance in absence of the user relevance judgments. In our approach we model the score associated with each document in the result set as a Gaussian random variable. The mean and the variance of each document score can then be used to estimate the probability that a document will be ranked above another one and thus calculate the expected rank of the document in the ranked list. We propose to measure the effectiveness of the system performance by comparing the predicted and actual ranks of the retrieved documents. In our experiments we consider two retrieval models and five document scoring methods and evaluate their impact on the proposed estimation measures. Our experiments with standardized data sets that include document relevance judgments and the task of predicting the relative query effectiveness show that the expected rank metric is robust to variations in document scoring and retrieval algorithms.