A Theoretical Analysis of NDCG Type Ranking Measures

A central problem in ranking is to design a ranking measure for evaluation of ranking functions. In this paper we study, from a theoretical perspective, the widely used Normalized Discounted Cumulative Gain (NDCG)-type ranking measures. Although there are extensive empirical studies of NDCG, little is known about its theoretical properties. We first show that, whatever the ranking function is, the standard NDCG which adopts a logarithmic discount, converges to 1 as the number of items to rank goes to infinity. On the first sight, this result is very surprising. It seems to imply that NDCG cannot differentiate good and bad ranking functions, contradicting to the empirical success of NDCG in many applications. In order to have a deeper understanding of ranking measures in general, we propose a notion referred to as consistent distinguishability. This notion captures the intuition that a ranking measure should have such a property: For every pair of substantially different ranking functions, the ranking measure can decide which one is better in a consistent manner on almost all datasets. We show that NDCG with logarithmic discount has consistent distinguishability although it converges to the same limit for all ranking functions. We next characterize the set of all feasible discount functions for NDCG according to the concept of consistent distinguishability. Specifically we show that whether NDCG has consistent distinguishability depends on how fast the discount decays, and 1/r is a critical point. We then turn to the cut-off version of NDCG, i.e., NDCG@k. We analyze the distinguishability of NDCG@k for various choices of k and the discount functions. Experimental results on real Web search datasets agree well with the theory.Comment: COLT 201

Evaluation Measures for Relevance and Credibility in Ranked Lists

Recent discussions on alternative facts, fake news, and post truth politics have motivated research on creating technologies that allow people not only to access information, but also to assess the credibility of the information presented to them by information retrieval systems. Whereas technology is in place for filtering information according to relevance and/or credibility, no single measure currently exists for evaluating the accuracy or precision (and more generally effectiveness) of both the relevance and the credibility of retrieved results. One obvious way of doing so is to measure relevance and credibility effectiveness separately, and then consolidate the two measures into one. There at least two problems with such an approach: (I) it is not certain that the same criteria are applied to the evaluation of both relevance and credibility (and applying different criteria introduces bias to the evaluation); (II) many more and richer measures exist for assessing relevance effectiveness than for assessing credibility effectiveness (hence risking further bias). Motivated by the above, we present two novel types of evaluation measures that are designed to measure the effectiveness of both relevance and credibility in ranked lists of retrieval results. Experimental evaluation on a small human-annotated dataset (that we make freely available to the research community) shows that our measures are expressive and intuitive in their interpretation

Unsupervised Graph-based Rank Aggregation for Improved Retrieval

This paper presents a robust and comprehensive graph-based rank aggregation approach, used to combine results of isolated ranker models in retrieval tasks. The method follows an unsupervised scheme, which is independent of how the isolated ranks are formulated. Our approach is able to combine arbitrary models, defined in terms of different ranking criteria, such as those based on textual, image or hybrid content representations. We reformulate the ad-hoc retrieval problem as a document retrieval based on fusion graphs, which we propose as a new unified representation model capable of merging multiple ranks and expressing inter-relationships of retrieval results automatically. By doing so, we claim that the retrieval system can benefit from learning the manifold structure of datasets, thus leading to more effective results. Another contribution is that our graph-based aggregation formulation, unlike existing approaches, allows for encapsulating contextual information encoded from multiple ranks, which can be directly used for ranking, without further computations and post-processing steps over the graphs. Based on the graphs, a novel similarity retrieval score is formulated using an efficient computation of minimum common subgraphs. Finally, another benefit over existing approaches is the absence of hyperparameters. A comprehensive experimental evaluation was conducted considering diverse well-known public datasets, composed of textual, image, and multimodal documents. Performed experiments demonstrate that our method reaches top performance, yielding better effectiveness scores than state-of-the-art baseline methods and promoting large gains over the rankers being fused, thus demonstrating the successful capability of the proposal in representing queries based on a unified graph-based model of rank fusions

Identification of functionally related enzymes by learning-to-rank methods

Enzyme sequences and structures are routinely used in the biological sciences as queries to search for functionally related enzymes in online databases. To this end, one usually departs from some notion of similarity, comparing two enzymes by looking for correspondences in their sequences, structures or surfaces. For a given query, the search operation results in a ranking of the enzymes in the database, from very similar to dissimilar enzymes, while information about the biological function of annotated database enzymes is ignored. In this work we show that rankings of that kind can be substantially improved by applying kernel-based learning algorithms. This approach enables the detection of statistical dependencies between similarities of the active cleft and the biological function of annotated enzymes. This is in contrast to search-based approaches, which do not take annotated training data into account. Similarity measures based on the active cleft are known to outperform sequence-based or structure-based measures under certain conditions. We consider the Enzyme Commission (EC) classification hierarchy for obtaining annotated enzymes during the training phase. The results of a set of sizeable experiments indicate a consistent and significant improvement for a set of similarity measures that exploit information about small cavities in the surface of enzymes