# Maximum Likelihood Estimation for Entity Ranking under Iterative Synthetic Data Augmentation

arXiv: https://arxiv.org/abs/2609.32987 · HTML: https://mlsanity.com/paper/2609.32987/

## Key facts

- Cited by 1 papers 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 (most cited first, 30 of 32)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [RLAIF vs. RLHF: Scaling Reinforcement Learning from Human Feedback with AI Feedback](https://mlsanity.com/paper/2309.00267/) (2023)
- [The Curse of Recursion: Training on Generated Data Makes Models Forget](https://mlsanity.com/paper/2305.17493/) (2023)
- [Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data](https://mlsanity.com/paper/2404.01413/) (2024)
- [Large Language Models Suffer From Their Own Output: An Analysis of the Self-Consuming Training Loop](https://mlsanity.com/paper/2311.16822/) (2023)
- [Collapse or Thrive? Perils and Promises of Synthetic Data in a Self-Generating World](https://mlsanity.com/paper/2410.16713/) (2024)
- [Reinforcement Learning from Human Feedback with Active Queries](https://mlsanity.com/paper/2402.09401/) (2024)
- [The Llama 4 Herd: Architecture, Training, Evaluation, and Deployment Notes](https://mlsanity.com/paper/2601.11659/) (2026)
- [Universality of the π2/6 Pathway in Avoiding Model Collapse](https://mlsanity.com/paper/2410.22812/) (2024)
- [Rate of Model Collapse in Recursive Training](https://mlsanity.com/paper/2412.17646/) (2024)
- [Model Collapse in the Self-Consuming Chain of Diffusion Finetuning: A Novel Perspective from Quantitative Trait Modeling](https://mlsanity.com/paper/2407.17493/) (2024)
- [Analyzing and Mitigating Model Collapse in Rectified Flow Models](https://mlsanity.com/paper/2412.08175/) (2024)
- [Recursive Learning Without Collapse: A Weighting-Based Stabilization Framework](https://mlsanity.com/paper/2502.18049/) (2025)
- [Uncertainty Quantification for Large Language Model Reward Learning under Heterogeneous Human Feedback](https://mlsanity.com/paper/2512.03208/) (2025)
- [Covariate Assisted Entity Ranking with Sparse Intrinsic Scores](https://mlsanity.com/paper/2407.08814/) (2024)
- [Confidence Diagram of Nonparametric Ranking for Uncertainty Assessment in Large Language Models Evaluation](https://mlsanity.com/paper/2412.05506/) (2024)
- [Uncertainty Quantification for Ranking with Heterogeneous Preferences](https://mlsanity.com/paper/2509.01847/) (2025)
- [Bias-Corrected Data Synthesis for Imbalanced Learning](https://mlsanity.com/paper/2510.26046/) (2025)
- [Recent advances in the Bradley--Terry Model: theory, algorithms, and applications](https://mlsanity.com/paper/2601.14727/) (2026)
- [Efficient Inference for Covariate-adjusted Bradley-Terry Model with Covariate Shift](https://mlsanity.com/paper/2503.18256/) (2025)
- [Quantifying Error Propagation and Model Collapse in Diffusion Models](https://mlsanity.com/paper/2602.16601/) (2026)
- [Calibeating Prediction-Powered Inference](https://mlsanity.com/paper/2604.21260/) (2026)
- [Fisher Random Walk: Automatic Debiasing Contextual Preference Inference for Large Language Model Evaluation](https://mlsanity.com/paper/2509.05852/) (2025)
- [Synthetic Augmentation in Imbalanced Learning: When It Helps, When It Hurts, and How Much to Add](https://mlsanity.com/paper/2601.16120/) (2026)
- [Harnessing Synthetic Data from Generative AI for Statistical Inference](https://mlsanity.com/paper/2603.05396/) (2026)
- [Generative modeling for the bootstrap](https://mlsanity.com/paper/2602.17052/) (2026)

## Built on by (most cited first, 1 of 1)

- [Graph-monotone entrywise guarantees for MLE and Rank Centrality on general comparison graphs](https://mlsanity.com/paper/2610.09030/) (2026)

## 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.