发表机构
University of Pennsylvania; University of Chicago（宾夕法尼亚大学; 芝加哥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在一般比较图上证明MLE和Rank Centrality的逐项误差界由图的代数连通度决定，且该界是图单调的，并扩展到异质采样和对抗性增广场景。
AI 中文摘要
成对比较被广泛用于推断潜在分数和识别排名靠前的项目。尽管在均匀采样下可获得尖锐的统计保证，但真实数据往往产生不规则的比较图，各对之间的观测次数异质。在本文中，我们在最小假设下研究任意固定比较图上的Bradley--Terry--Luce模型。我们证明标准最大似然估计器和Rank Centrality都能达到阶为$1/\sqrt{\lambda_{\mathcal{D}}}$的高概率逐项误差率（直至对数因子和动态范围因子），其中$\lambda_{\mathcal{D}}$是计数加权观测图的代数连通度。该保证是图单调的，因为当添加额外比较时$\lambda_{\mathcal{D}}$不会减少。在异质采样下，即比较对以不等的概率独立采样时，我们的保证改进了现有误差界或需要更弱的假设。我们进一步扩展分析，表明两种估计器对结果自适应增广具有鲁棒性，其中对手可以在观察初始结果后选择额外的比较对。
英文摘要
Pairwise comparisons are widely used to infer latent scores and identify top-ranked items. Although sharp statistical guarantees are available under uniform sampling, real data often induce irregular comparison graphs with heterogeneous observation counts across pairs. In this paper, we study an arbitrary fixed comparison graph under the Bradley--Terry--Luce model with minimal assumptions. We prove that both the standard maximum likelihood estimator and Rank Centrality achieve a high-probability entrywise error rate of order $1/\sqrt{λ_{\mathcal{D}}}$ up to logarithmic and dynamic-range factors, where $λ_{\mathcal{D}}$ is the algebraic connectivity of the count-weighted observation graph. This guarantee is graph-monotone since $λ_{\mathcal{D}}$ cannot decrease when additional comparisons are added. Under heterogeneous sampling, where comparison pairs are sampled independently with unequal probabilities, our guarantee improves existing error bounds or requires weaker assumptions. We further extend our analysis to show that both estimators are robust against outcome-adaptive augmentation, where an adversary can choose additional comparison pairs after observing the initial outcomes.
