期刊
ANNALS OF STATISTICS
卷 48, 期 2, 页码 1072-1097出版社
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/19-AOS1838
关键词
Pairwise comparisons; strong stochastic transitivity; structured matrix completion
资金
- NSF [AST-144078, ECCS-1343398, DMS-1612948, CCF-1528132, CCF-1704967, CCF-0939370]
- DOD Advanced Research Projects Agency [W911NF-16-1-0552]
- DOD Office of Naval Research [N00014-18-1-2640]
- NSF CAREER Grant [DMS-1541099]
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 computationally efficient 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. We also provide explicit classes of graphs for which the rates achieved by these estimators are optimal. Our results are corroborated by simulations on multiple comparison topologies.
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