mlsanityData to 14 Oct 2026

Maximum Likelihood Estimation for Entity Ranking under Iterative Synthetic Data Augmentation

arXiv 2609.32987 ↗First posted 26 Sep 2026stat.ME math.ST stat.MLcited by 1

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Abstract (arXiv)

We study entity ranking and inference under the Bradley--Terry--Luce (BTL) model using pairwise comparisons collected over sparse comparison graphs. In practice, collecting high-quality human judgments can be expensive and time-consuming, motivating the use of synthetic data augmentation in model training. We analyze an iterative synthetic augmentation workflow in which synthetic comparisons generated from fitted models are successively added to the original dataset. In this process, the proportion of real data may vanish as the number of iterations grows. However, emerging literature has shown that recursive training on synthetic data can lead to model collapse, raising concerns about the statistical reliability of such augmentation procedures. To this end, we systematically analyze the resulting MLE in finite-sample, high-dimensional regimes. For the resulting iterative maximum likelihood estimator (MLE), we derive its optimal finite-sample ℓ2 and ℓ∞ statistical rates and establish its asymptotic normality under natural identifiability conditions. We further characterize regimes in which model collapse is avoided despite the diminishing fraction of real data. We validate our theoretical findings through large-scale numerical experiments and an application to the Arena Human Preference 140k dataset.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 32 of its 97 references that are in the map. First posted on arXiv 26 Sep 2026.

Builds on

32 of 97 references.

References · 32

  1. 2024The Llama 3 Herd of Modelscited by 14,715
  2. 2023LLaMA: Open and Efficient Foundation Language Modelscited by 14,132
  3. 2023Llama 2: Open Foundation and Fine-Tuned Chat Modelscited by 13,028
  4. 2022Constitutional AI: Harmlessness from AI Feedbackcited by 3,050
  5. 2024Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preferencecited by 1,184
  6. 2023RLAIF vs. RLHF: Scaling Reinforcement Learning from Human Feedback with AI Feedbackcited by 625
  7. 2023The Curse of Recursion: Training on Generated Data Makes Models Forgetcited by 356
  8. 2024Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Datacited by 151
  9. 2023Large Language Models Suffer From Their Own Output: An Analysis of the Self-Consuming Training Loopcited by 79
  10. 2024Collapse or Thrive? Perils and Promises of Synthetic Data in a Self-Generating Worldcited by 52
  11. 2024Reinforcement Learning from Human Feedback with Active Queriescited by 43
  12. 2026The Llama 4 Herd: Architecture, Training, Evaluation, and Deployment Notescited by 30
20 more
  1. 2024Universality of the π2/6 Pathway in Avoiding Model Collapsecited by 26
  2. 2024Rate of Model Collapse in Recursive Trainingcited by 25
  3. 2024Model Collapse in the Self-Consuming Chain of Diffusion Finetuning: A Novel Perspective from Quantitative Trait Modelingcited by 12
  4. 2024Analyzing and Mitigating Model Collapse in Rectified Flow Modelscited by 11
  5. 2025Recursive Learning Without Collapse: A Weighting-Based Stabilization Frameworkcited by 10
  6. 2025Uncertainty Quantification for Large Language Model Reward Learning under Heterogeneous Human Feedbackcited by 9
  7. 2024Covariate Assisted Entity Ranking with Sparse Intrinsic Scorescited by 7
  8. 2024Confidence Diagram of Nonparametric Ranking for Uncertainty Assessment in Large Language Models Evaluationcited by 6
  9. 2025Uncertainty Quantification for Ranking with Heterogeneous Preferencescited by 6
  10. 2025Bias-Corrected Data Synthesis for Imbalanced Learningcited by 6
  11. 2026Recent advances in the Bradley--Terry Model: theory, algorithms, and applicationscited by 6
  12. 2025Efficient Inference for Covariate-adjusted Bradley-Terry Model with Covariate Shiftcited by 4
  13. 2026Quantifying Error Propagation and Model Collapse in Diffusion Modelscited by 4
  14. 2026Calibeating Prediction-Powered Inferencecited by 4
  15. 2025Fisher Random Walk: Automatic Debiasing Contextual Preference Inference for Large Language Model Evaluationcited by 3
  16. 2026Synthetic Augmentation in Imbalanced Learning: When It Helps, When It Hurts, and How Much to Addcited by 3
  17. 2026Harnessing Synthetic Data from Generative AI for Statistical Inferencecited by 3
  18. 2026Generative modeling for the bootstrapcited by 2
  19. 2026Perturbation is All You Need for Extrapolating Language Modelscited by 2
  20. 2026When Does Model Collapse Occur in Structured Interactive Learning?cited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Graph-monotone entrywise guarantees for MLE and Rank Centrality on general comparison graphscited by 0

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