Comparing two binned probability distributions for information access evaluation

Some modern information access tasks such as natural language dialogue tasks are difficult to evaluate, for often there is no such thing as the ground truth: different users may have different opinions about the system's output. A few task designs for dialogue evaluation have been implemented and/or proposed recently, where both the ground truth data and the system's output are represented as a distribution of users' votes over bins on a non-nominal scale. The present study first points out that popular bin-by-bin measures such as Jensen-Shannon divergence and Sum of Squared Errors are clearly not adequate for such tasks, and that cross-bin measures should be used. Through experiments using artificial distributions as well as real ones from a dialogue evaluation task, we demonstrate that two cross-bin measures, namely, the Normalised Match Distance (NMD; a special case of the Earth Mover's Distance) and the Root Symmetric Normalised Order-aware Divergence (RSNOD), are indeed substantially different from the bin-by-bin measures.Furthermore, RSNOD lies between the popular bin-by-bin measures and NMD in terms of how it behaves. We recommend using both of these measures in the aforementioned type of evaluation tasks.