Detecting Abrupt Changes in Sequential Pairwise Comparison Data

TL;DR

This paper introduces algorithms for detecting change points in time-evolving pairwise comparison data modeled by the Bradley-Terry-Luce framework, enabling accurate localization of ranking shifts in high-dimensional settings.

Contribution

It proposes novel dynamic programming algorithms for consistent change point detection in non-stationary BTL models with theoretical guarantees.

Findings

Algorithms accurately identify change points in simulations.

Theoretical rates depend on model parameters and change magnitudes.

Validated with real-world data examples.

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.