# Uncertainty Quantification for Prior-Data Fitted Networks using Martingale Posteriors

arXiv: https://arxiv.org/abs/2505.11325 · HTML: https://mlsanity.com/paper/2505.11325/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 16 of 16)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [What Can Transformers Learn In-Context? A Case Study of Simple Function Classes](https://mlsanity.com/paper/2208.01066/) (2022)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [Transformers Can Do Bayesian Inference](https://mlsanity.com/paper/2112.10510/) (2021)
- [TabICL: A Tabular Foundation Model for In-Context Learning on Large Data](https://mlsanity.com/paper/2502.05564/) (2025)
- [Subspace Inference for Bayesian Deep Learning](https://mlsanity.com/paper/1907.07504/) (2019)
- [Statistical Foundations of Prior-Data Fitted Networks](https://mlsanity.com/paper/2305.11097/) (2023)
- [Retrieval & Fine-Tuning for In-Context Tabular Models](https://mlsanity.com/paper/2406.05207/) (2024)
- [Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspective](https://mlsanity.com/paper/2406.00793/) (2024)
- [LLM Processes: Numerical Predictive Distributions Conditioned on Natural Language](https://mlsanity.com/paper/2405.12856/) (2024)
- [TuneTables: Context Optimization for Scalable Prior-Data Fitted Networks](https://mlsanity.com/paper/2402.11137/) (2024)
- [Martingale posterior distributions](https://mlsanity.com/paper/2103.15671/) (2021)
- [TabPFN Unleashed: A Scalable and Effective Solution to Tabular Classification Problems](https://mlsanity.com/paper/2502.02527/) (2025)
- [Can Transformers Learn Full Bayesian Inference in Context?](https://mlsanity.com/paper/2501.16825/) (2025)
- [Quasi-Bayes meets Vines](https://mlsanity.com/paper/2406.12764/) (2024)

## Built on by (most cited first, 5 of 5)

- [TabMGP: Martingale Posterior with TabPFN](https://mlsanity.com/paper/2510.25154/) (2025)
- [What does a Bayes-filtered transformer believe? A predictive Monte Carlo approach](https://mlsanity.com/paper/2607.17060/) (2026)
- [Variational predictive resampling](https://mlsanity.com/paper/2605.11168/) (2026)
- [Can Tabular Foundation Models Amortize Statistical Inference?](https://mlsanity.com/paper/2609.33114/) (2026)
- [How Well Do Prior-Data Fitted Networks Amortize Bayesian Inference?](https://mlsanity.com/paper/2610.13764/) (2026)

## Abstract (arXiv)

Prior-data fitted networks (PFNs) have emerged as promising foundation models for prediction from tabular datasets, achieving state-of-the-art performance on small to moderate data sizes without tuning. While PFNs are motivated by Bayesian ideas, they do not provide any uncertainty quantification for predictive means, quantiles, or similar quantities. We propose a principled, efficient, and tuning-free sampling procedure to construct Bayesian posteriors for such estimates based on martingale posteriors, and prove its convergence. Several simulated and real-world data examples showcase the efficiency and calibration of our method in inference applications.