Graph-monotone entrywise guarantees for MLE and Rank Centrality on general comparison graphs
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.
ProofPaper ↗
Key points
- 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 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.
Sources (1)
- [1]Graph-monotone entrywise guarantees for MLE and Rank Centrality on general comparison graphsarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 6, 07:30 PM
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.
Pairwise comparisons are widely used to infer latent scores and identify top-ranked items.
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