# Probabilistic Reasoning with LLMs for k-anonymity Estimation

arXiv: https://arxiv.org/abs/2503.09674 · HTML: https://mlsanity.com/paper/2503.09674/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 2 of its 94 references that are in the map.
- First posted on arXiv 12 Mar 2025.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)

## Builds on (most cited first, 2 of 2)

- [MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning](https://mlsanity.com/paper/2310.03731/) (2023)
- [Let's Think Var-by-Var: Large Language Models Enable Ad Hoc Probabilistic Reasoning](https://mlsanity.com/paper/2412.02081/) (2024)

## Built on by (most cited first, 2 of 2)

- [ReThinker: Scientific Reasoning by Rethinking with Guided Reflection and Confidence Control](https://mlsanity.com/paper/2602.04496/) (2026)
- [Beyond Direct Identifiers: Probabilistic Privacy Risk Estimation for Privacy-Conscious LLM Query Delegation](https://mlsanity.com/paper/2608.09140/) (2026)

## Abstract (arXiv)

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.