Copulas for information retrieval

In many domains of information retrieval, system estimates of document relevance are based on multidimensional quality criteria that have to be accommodated in a unidimensional result ranking. Current solutions to this challenge are often inconsistent with the formal probabilistic framework in which constituent scores were estimated, or use sophisticated learning methods that make it difficult for humans to understand the origin of the final ranking. To address these issues, we introduce the use of copulas, a powerful statistical framework for modeling complex multi-dimensional dependencies, to information retrieval tasks. We provide a formal background to copulas and demonstrate their effectiveness on standard IR tasks such as combining multidimensional relevance estimates and fusion of results from multiple search engines. We introduce copula-based versions of standard relevance estimators and fusion methods and show that these lead to significant performance improvements on several tasks, as evaluated on large-scale standard corpora, compared to their non-copula counterparts. We also investigate criteria for understanding the likely effect of using copula models in a given retrieval scenario.