Bias-variance decomposition of IR evaluation

It has been recognized that, when an information retrieval (IR) system achieves improvement in mean retrieval effectiveness (e.g. mean average precision (MAP)) over all the queries, the performance (e.g., average precision (AP)) of some individual queries could be hurt, resulting in retrieval instability. Some stability/robustness metrics have been proposed. However, they are often defined separately from the mean effectiveness metric. Consequently, there is a lack of a unified formulation of effectiveness, stability and overall retrieval quality (considering both). In this paper, we present a unified formulation based on the bias-variance decomposition. Correspondingly, a novel evaluation methodology is developed to evaluate the effectiveness and stability in an integrated manner. A case study applying the proposed methodology to evaluation of query language modeling illustrates the usefulness and analytical power of our approach.