Title: Preference-Based Dynamic Ranking Structure Recognition
Venue: NeurIPS 2025
Accepted: yes
Keywords: dynamic ranking

Bradley-Terry model

structural change detection

preference-based data

clustering
Abstract: Preference-based data often appear complex and noisy but may conceal underlying homogeneous structures. This paper introduces a novel framework of ranking structure recognition for preference-based data. We first develop an approach to identify dynamic ranking groups by incorporating temporal penalties into a spectral estimation for the celebrated Bradley-Terry model. To detect structural changes, we introduce an innovative objective function and present a practicable algorithm based on dynamic programming. Theoretically, we establish the consistency of ranking group recognition by exploiting properties of a random 'design matrix' induced by a reversible Markov chain. We also tailor a group inverse technique to quantify the uncertainty in item ability estimates. Additionally, we prove the consistency of  structure change recognition, ensuring the robustness of the proposed framework. Experiments on both synthetic and real-world datasets demonstrate the practical utility and interpretability of our approach.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a method for recognizing dynamic ranking structures in preference-based data, where instead of fixed scores, pairwise comparisons evolve over time.The authors build on the Bradley-Terry model and develop a technique that can:\n- Group items that behave similarly over a time interval,\n- Track how those groups change over time, and\n- Rank the groups and their members in a meaningful way.\nThey tackle the challenges of noisy, time-varying data by combining spectral methods with optimization tricks like adaptive group lasso. \nExperiments on NBA data show that their method produces interpretable, accurate rankings and captures real-world structural shifts like team trades.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- The paper introduces a dynamic framework for ranking and grouping, which is a step beyond static models and is very practical in real-world utility.\n- The proposed method combines spectral methods, adaptive group lasso, and dynamic programming in a coherent way, and apprears to be theoratically guaranteed for group recognition and change point detection.\n\nWeaknesses:\n- The paper is very hard to read with multiple theorems, remarks, assumptions. This creates barriers for reader from understanding the content. Apart from this, one of the main contribution is confusing in lacking explanation of the terms \"consistency recognition of groups\", \"structure recognition consistency\", \"uncertainty of item ability estimators\". In addition, the figures are hard to read with font size being too small. Overall, I find great space left to improve the readability of the paper.\n- An essential weakness of the paper is its strong reliance on smoothness and homogeneity assumptions in the latent ability trajectories. The method assumes that items within a group have similar, smoothly varying abilities over time, which may not hold in many real-world scenarios, especially in volatile domains like finance, user preferences, or competitive gaming. This assumption is critical to both the group identification and change point detection. If it is violated, the model's validity and interpretability could break down.\n\nQUESTIONS:\nNA\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 1, "IMPACT": 2, "ORIGINALITY": 4, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper considers the problem of ranking structure recognition for preference-based data under the Bradley-Terry model, where the ranking structure could undergo changes over time. It first studies ranking group recovery for a given interval by introducing an optimization objective that can be formulated as the group lasso problem. Then, it applies the proposed clustering method to recognition of group changes by considering a combinatorial optimization problem. An algorithm based on dynamic programming is developed. Under certain technical assumptions, recognition consistency and estimator uncertainty results are established. Computational experiments are provided to evaluate the proposed framework.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\nThe work proposes a framework for analyzing ranking structure recognition where the underlying cluster structure may experience changes, which is interesting and has potential applications to various areas.\nIt designs an objective function that allows for recovering the unknown change point of structures, and develops a DP-based algorithm to solve the combinatorial problem. I found this part inspiring.\nWeakness:\nWhile Theorem 3.6 quantifies the uncertainty of item ability estimations, can you comment on the optimality of the result?\nNonasymptotic recovery guarantees have received considerable attention in the recent literature of ranking. Do you expect such guarantees to hold for your proposed method?\nSome notation choices may cause confusion for readers. For instance, on line 85: “\\|f(t)\\|_{2,T}=..., where $f(t)$ is a function on $[0,T]$”. Typically, $f(t)$ is perceived as a value and it might be more appropriate to use $f$ inside the norm.\nOn line 129: would it be ““induced by \\tilde{\\pi}” instead?\n\nQUESTIONS:\nSee above.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a novel framework for dynamic ranking structure recognition based on the Bradley-Terry model. It simultaneously identifies item groups with similar time-varying rankings and detects structural changes over time using a spectral estimation method combined with temporal penalties. The authors design an efficient optimization procedure using adaptive group lasso and dynamic programming, and provide theoretical guarantees for consistency and asymptotic distribution. Experiments on synthetic data and NBA game results demonstrate the method’s effectiveness and interpretability.\n\nSTRENGTHS AND WEAKNESSES:\nStrength:\n\nThis paper tries to tack the fundmental problem - how to track groups and rankings that change over time using preference data.  It introduces a novel, separable objective function that enables efficient optimization via dynamic programming. Theoretical results, including consistency and uncertainty quantification, are rigorously established. Empirical evaluations on synthetic and real-world datasets (e.g., NBA games) show that the proposed method outperforms existing baselines in both accuracy and interpretability.\n\n\n\nWeakness:\n\nThe main weakness so far lies in the presentation. While the theoretical sections are mathematically sound, they are dense and lack intuitive explanation, making the paper difficult to follow. Including a complete notation table and illustrative diagrams could significantly enhance clarity. \n\nAdditionally, the authors mention using cross-validation to select hyperparameters—how sensitive is the method to these choices?\n\nQUESTIONS:\n1. Can the authors add one additional pargraph to briefly define the \"group change\",possibly with illustrative examples to enhance clarity?\n\n2. Can the authors conduct additional experiments to evaluate the sensitivity of the method to hyperparameter choices?\n\nLIMITATIONS:\nThe authors point out the limitation of current formulation only focuses on pairwise comparison, leaving the extension to multiple candidates open.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors describe a statistical method to estimate a dynamic ranking structure in preference data. The Bradley-Terry model is used for inferring latent preference scores. Items are grouped together based on similar temporal behavior in their preferences. Given a grouping structure, the ranking order of these groups is determined. One of the goals of this study addresses the question how significant changes in the preference structure can be detected.\n\nThe method improves over SOTA techniques by higher accuracy and enhanced interpretability.\n\nThe objective function for scoring seems to be novel and it is designed to be solved by dynamic programming which guarantees efficient solutions. The Ranking Structure Recognition of NBA Teams shows fairly rapid changes in group structure associated with trading windows or the end of a season (see fig 2).\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nObserving dynamic preferences requires a complex dynamics on the symmetric group to estimate a partial ranking. It couples grouping of objects when they are indistinguishable and ranking the resulting different groups. The model seems to perform well in applications when compared to SOTA methods.\n\nThe authors statistically analyze the group estimates $\\hat{G}$ and prove consistency (Th 3.3) and asymptotic normality (Th 3.6). I find this analysis convincing. \n\nThe authors claim priority on the ranking structure changes for the BT model. The proposed objective function can be efficiently solved by dynamic programming due to its \"separable properties\". The experimental results document the improvements over SOTA results for group change detection. \n\n\nWeaknesses:\n\nThe paper seems to be a compressed version of a longer manuscript and it reads a bit overloaded. I had to search together the definitions to understand the essence of the objective function and some of the statistical arguments. \n\n- Some of the symbols are not clear, e.g., where is $\\tilde{S}_k$ defined.\n\n- It is also unclear (to me) why the normalization of the refit estimator in eq (2.3) scales with the absolute group size $|\\hat G_k|$ and not with the relative group size.\n\n- Algorithm 1 does not introduce a symbol for the observed data. I assumed it to be $mathcal{Y}$. Please add it to specify the data in the algorithm.\n\n- The objective function (2.1) could be described in more detail. The first part seems to measure deviations from stationarity, while the $\\lambda$ scaled part regularizes the inference. Why are ratios of item score differences proposed as regularization term? The regularization term often refers to the corresponding noise process of the function to be determined by variation. Does there exist such an interpretation for the second term in (2.1)?\n\nQUESTIONS:\nIn this paper, the basic assumption of the Bradlex-Terry model requires independence of the pair-wise preferences $y_{ij}(t_k) \\in \\mathcal{Y}$. How well does this assumption hold for real world preference data? It would be helpful for the reader to discuss the applicability of the BT model for today's applications. \n\nWhy does the normalization of the refit estimator in eq (2.3) scale with the absolute group size $|\\hat G_k|$ and not with the relative group size? \n\nWhat are the \"separable properties\" in the objective function that admit dynamic programming as a solution strategy? There seems to be only one occurence of \"separable\" in the manuscript stating the claim; but no explanation is given\nwhy \"separable properties\" enable dynamic programming.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-07"}