Probabilistic Reasoning with LLMs for k-anonymity Estimation

Probabilistic reasoning is a key aspect of both human and artificial intelligence that allows for handling uncertainty and ambiguity in decision-making. In this paper, we introduce a new numerical reasoning task under uncertainty for large language models, focusing on estimating the privacy risk of user-generated documents containing privacy-sensitive information. We propose BRANCH, a new LLM methodology that estimates the k-privacy value of a text-the size of the population matching the given information. BRANCH factorizes a joint probability distribution of personal information as random variables. The probability of each factor in a population is estimated separately using a Bayesian network and combined to compute the final k-value. Our experiments show that this method successfully estimates the k-value 73% of the time, a 13% increase compared to o3-mini with chain-of-thought reasoning. We also find that LLM uncertainty is a good indicator for accuracy, as high-variance predictions are 37.47% less accurate on average.

@article{zheng2025_2503.09674,
  title={ Probabilistic Reasoning with LLMs for k-anonymity Estimation },
  author={ Jonathan Zheng and Sauvik Das and Alan Ritter and Wei Xu },
  journal={arXiv preprint arXiv:2503.09674},
  year={ 2025 }
}