Detecting Abrupt Changes in Sequential Pairwise Comparison Data

Wanshan Li, Alessandro Rinaldo, Daren Wang

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

TL;DR: We propose novel and practicable algorithms that can localize change points in pairwise comparison data with time stamps modeled by the Bradley-Terry model and establish consistency rates for our methodology.

Abstract: 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.