Modeling score distributions in information retrieval

We review the history of modeling score distributions, focusing on the mixture of normal-exponential by investigating the theoretical as well as the empirical evidence supporting its use. We discuss previously suggested conditions which valid binary mixture models should satisfy, such as the Recall-Fallout Convexity Hypothesis, and formulate two new hypotheses considering the component distributions, individually as well as in pairs, under some limiting conditions of parameter values. From all the mixtures suggested in the past, the current theoretical argument points to the two gamma as the most-likely universal model, with the normal-exponential being a usable approximation. Beyond the theoretical contribution, we provide new experimental evidence showing vector space or geometric models, and BM25, as being 'friendly' to the normal-exponential, and that the non-convexity problem that the mixture possesses is practically not severe. Furthermore, we review recent non-binary mixture models, speculate on graded relevance, and consider methods such as logistic regression for score calibration.