Optimal data collection for informative rankings expose well-connected graphs

Braxton Osting, Christoph Brune, Stanley J. Osher

    Research output: Contribution to journalArticleAcademicpeer-review

    11 Citations (Scopus)
    58 Downloads (Pure)

    Abstract

    Given a graph where vertices represent alternatives and arcs represent pairwise comparison data, the statistical ranking problem is to find a potential function, defined on the vertices, such that the gradient of the potential function agrees with the pairwise comparisons. Our goal in this paper is to develop a method for collecting data for which the least squares estimator for the ranking problem has maximal Fisher information. Our approach, based on experimental design, is to view data collection as a bi-level optimization problem where the inner problem is the ranking problem and the outer problem is to identify data which maximizes the informativeness of the ranking. Under certain assumptions, the data collection problem decouples, reducing to a problem of finding multigraphs with large algebraic connectivity. This reduction of the data collection problem to graph-theoretic questions is one of the primary contributions of this work. As an application, we study the Yahoo! Movie user rating data set and demonstrate that the addition of a small number of well-chosen pairwise comparisons can significantly increase the Fisher informativeness of the ranking. As another application, we study the 2011-12 NCAA football schedule and propose schedules with the same number of games which are significantly more informative. Using spectral clustering methods to identify highly-connected communities within the division, we argue that the NCAA could improve its notoriously poor rankings by simply scheduling more out-of- conference games.
    Original languageUndefined
    Pages (from-to)2981-3012
    Number of pages32
    JournalJournal of machine learning research
    Volume15
    Publication statusPublished - Oct 2014

    Keywords

    • EWI-25598
    • optimal experimental design
    • graph synthesis
    • ranking
    • Active learning
    • Scheduling
    • METIS-309830
    • IR-93780
    • algebraic connectivity

    Cite this