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Preference-Based Dynamic Ranking Structure Recognition
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Proposes dynamic ranking-group recognition for time-varying Bradley-Terry models via temporally penalized kernel spectral estimation, plus a dynamic-programming method for detecting group-structure change points, with consistency theory and NBA experiments.
Problem
Ranking items from time-varying pairwise comparisons when latent ability groups exist and their membership can change over time; the goal is to recover dynamic ranking groups and detect when group structure changes.
Approach
Combines a kernel-based Markov-chain (rank centrality style) estimator of time-varying BT scores with a fused-lasso-type group penalty solved as an adaptive group lasso, then detects structural change points by a penalized partition objective solved with dynamic programming over candidate change points.
Key results
- In simulations, the proposed method's Kendall tau reaches 0.9998-1.0000 in Setting 1 and 0.9416-0.9683 in Setting 2, versus 0.7974-0.7977 for GRC in Setting 2.
- Structure change detection Hausdorff distance drops to 0.0000-0.0076 for Mh=10 and above, versus 0.1333-0.2842 for the naive baseline.
- On NBA data, the method identifies two structure change points (2015-2016 trade deadline and end of 2016-2017 season) with cross-validated gamma1=0.04 and gamma2=0.006.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the refit strategy after identifying ranking groups (ablation) | Ours dynamic ranking method · Simulation setting 1 and setting 2 | MSE: 0.0586 -> 0.0466; 0.0421 -> 0.0375; 0.0494 -> 0.0359; 0.0291 -> 0.0250 | Helped |
| Use the refit strategy after identifying ranking groups (ablation) | Ours dynamic ranking method · Simulation setting 1 and setting 2 | Kendall τ: 0.9998 -> 0.9998; 1.0000 -> 1.0000; 0.9416 -> 0.9484; 0.9644 -> 0.9683 | Helped |
| Use dynamic grouping and ranking rather than KRC | Ours dynamic ranking method · Setting 1 and setting 2 | Kendall τ: 0.8330 -> 0.9998; 0.8207 -> 1.0000; 0.7565 -> 0.9416; 0.7742 -> 0.9644 | Helped |
| Use the proposed structural change detector rather than the naive adjacent-interval baseline | Structure change detection · Setting 1 and setting 2 | Hausdorff distance: 0.2084 -> 0.0051; 0.1800 -> 0.0004; 0.1333 -> 0.0000; 0.3258 -> 0.0492; 0.2842 -> 0.0076; 0.2434 -> 0.0004 | Helped |
| Increase the amount of observed data | Proposed structure change detector · Setting 1 and setting 2 | Hausdorff distance: 0.0051 -> 0.0004 -> 0.0000; 0.0492 -> 0.0076 -> 0.0004 | Helped |
| Apply static grouping rather than dynamic grouping | GRC · Setting 2 | Specificity: 100.00% vs 63.64%; 100.00% vs 63.71% | Hurt |
Surprising findings
- Static GRC fails to distinguish some groups in the dynamic Setting 2 (specificity 63.64%), showing the need for a dynamic model.
Limitations
- Only pairwise comparisons are handled; multi-way comparisons are left to future work.
- Hyperparameter selection lacks an established information-criterion rule; cross-validation is used.
- Theoretical guarantees rely on assumptions such as bounded score ratios and specific rates for group separation and within-group variation.
Experimental setup
Datasets: NBA regular season results 2014-2015 to 2018-2019 (nba.com)
Benchmarks: simulated dynamic BT settings NBA 2014-2019 game results
Metrics: Kendall tau MSE sensitivity specificity change point count Hausdorff distance
Baselines: Group Rank Centrality (GRC) Kernel Rank Centrality (KRC) naive per-interval grouping
Builds on: Bradley-Terry model Rank Centrality Group Rank Centrality fused lasso
Closest papers by meaning
- Conditional independence and graphical models for rankings (NeurIPS 2026 · similarity 0.85)
- Data-driven Rank Breaking for Efficient Rank Aggregation (ICML 2016 · similarity 0.85)
- Inductive Pairwise Ranking: Going Beyond the n log(n) Barrier (AAAI 2017 · similarity 0.85)
- Robust Consensus in Ranking Data Analysis: Definitions, Properties and Computational Issues (ICML 2023 · similarity 0.84)
- Stability and Multigroup Fairness in Ranking with Uncertain Predictions (ICML 2024 · similarity 0.83)
- Active preference learning for ordering items in- and out-of-sample (NeurIPS 2024 · similarity 0.83)
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