Optimal Data Collection For Informative Rankings Expose Well-Connected Graphs
Braxton Osting, Christoph Brune, Stanley J. Osher

TL;DR
This paper develops a graph-theoretic approach to optimize data collection for ranking problems, maximizing Fisher information through strategic pairwise comparisons, with applications to movie ratings and sports schedules.
Contribution
It introduces a bi-level optimization framework that reduces data collection to finding highly connected graphs, enhancing ranking informativeness.
Findings
Adding well-chosen comparisons increases Fisher information.
Optimized schedules improve ranking accuracy.
Graph connectivity correlates with ranking quality.
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…
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Taxonomy
TopicsSports Analytics and Performance · Complex Network Analysis Techniques · Transportation Planning and Optimization
