Worst-case vs Average-case Design for Estimation from Fixed Pairwise Comparisons

Abstract

Pairwise comparison data arises in many domains, including tournament rankings, web search, and preference elicitation. Given noisy comparisons of a fixed subset of pairs of items, we study the problem of estimating the underlying comparison probabilities under the assumption of strong stochastic transitivity (SST). We also consider the noisy sorting subclass of the SST model. We show that when the assignment of items to the topology is arbitrary, these permutation-based models, unlike their parametric counterparts, do not admit consistent estimation for most comparison topologies used in practice. We then demonstrate that consistent estimation is possible when the assignment of items to the topology is randomized, thus establishing a dichotomy between worst-case and average-case designs. We propose two estimators in the average-case setting and analyze their risk, showing that it depends on the comparison topology only through the degree sequence of the topology. The rates achieved by these estimators are shown to be optimal for a large class of graphs. Our results are corroborated by simulations on multiple comparison topologies.

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Cited by in corpus (7)

• Spectral Method and Regularized MLE Are Both Optimal for Top-$K$ Ranking
• Poisoning Attack against Estimating from Pairwise Comparisons
• Lagrangian Inference for Ranking Problems
• Minimax Rates and Efficient Algorithms for Noisy Sorting
• Learning from Comparisons and Choices
• Breaking the $1/\sqrt{n}$ Barrier: Faster Rates for Permutation-based Models in Polynomial Time
• Graph Resistance and Learning from Pairwise Comparisons