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Detecting Abrupt Changes in Sequential Pairwise Comparison Data
Wanshan Li · Alessandro Rinaldo · Daren Wang

Tue Dec 06 09:00 AM -- 11:00 AM (PST) @
in Lightning Talks 1B-4 »

The Bradley-Terry-Luce (BTL) model is a classic and very popular statistical approach for eliciting a global ranking among a collection of items using pairwise comparison data. In applications in which the comparison outcomes are observed as a time series, it is often the case that data are non-stationary, in the sense that the true underlying ranking changes over time. In this paper we are concerned with localizing the change points in a high-dimensional BTL model with piece-wise constant parameters. We propose novel and practicable algorithms based on dynamic programming that can consistently estimate the unknown locations of the change points. We provide consistency rates for our methodology that depend explicitly on the model parameters, the temporal spacing between two consecutive change points and the magnitude of the change. We corroborate our findings with extensive numerical experiments and a real-life example.

Keywords: high-dimensional statistics · Bradley-Terry model · change point detection · ranking

Author Information

Wanshan Li (Carnegie Mellon University)
Alessandro Rinaldo (CMU)
Daren Wang (University of Chicago)

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