论文标题
检测顺序成对比较数据的突然变化
Detecting Abrupt Changes in Sequential Pairwise Comparison Data
论文作者
论文摘要
Bradley-terry-luce（BTL）模型是一种经典且非常流行的统计方法，用于使用成对比较数据在项目集合中引起全球排名。在观察到比较结果为时间序列的应用中，通常情况下，数据是非平稳的，从某种意义上说，真正的基础排名会随着时间的推移而变化。在本文中，我们关注的是将变更点定位在具有零件恒定参数的高维BTL模型中。我们根据动态编程提出了新颖和可行的算法，该算法可以始终如一地估计变更点的未知位置。我们为我们的方法提供一致性率，该方法明确取决于模型参数，两个连续变更点之间的时间间距和变化的幅度。我们通过广泛的数值实验和现实生活中的例子来证实我们的发现。
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.
