mlsanityData to 14 Oct 2026

Uncertainty Quantification for Prior-Data Fitted Networks using Martingale Posteriors

arXiv 2505.11325 ↗First posted 16 May 2025stat.ME cs.AI cs.LGcited by 5

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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.

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

16 of 40 references.

References · 16

  1. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,926
  2. 2019Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methodscited by 913
  3. 2022What Can Transformers Learn In-Context? A Case Study of Simple Function Classescited by 715
  4. 2022TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Secondcited by 674
  5. 2021Transformers Can Do Bayesian Inferencecited by 360
  6. 2025TabICL: A Tabular Foundation Model for In-Context Learning on Large Datacited by 289
  7. 2019Subspace Inference for Bayesian Deep Learningcited by 95
  8. 2023Statistical Foundations of Prior-Data Fitted Networkscited by 65
  9. 2024Retrieval & Fine-Tuning for In-Context Tabular Modelscited by 59
  10. 2024Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspectivecited by 57
  11. 2024LLM Processes: Numerical Predictive Distributions Conditioned on Natural Languagecited by 55
  12. 2024TuneTables: Context Optimization for Scalable Prior-Data Fitted Networkscited by 47
4 more
  1. 2021Martingale posterior distributionscited by 45
  2. 2025TabPFN Unleashed: A Scalable and Effective Solution to Tabular Classification Problemscited by 36
  3. 2025Can Transformers Learn Full Bayesian Inference in Context?cited by 31
  4. 2024Quasi-Bayes meets Vinescited by 5

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 4.

5 papers.

  1. 2025TabMGP: Martingale Posterior with TabPFNcited by 9
  2. 2026What does a Bayes-filtered transformer believe? A predictive Monte Carlo approachcited by 1
  3. 2026Variational predictive resamplingcited by 0
  4. 2026Can Tabular Foundation Models Amortize Statistical Inference?cited by 0
  5. 2026How Well Do Prior-Data Fitted Networks Amortize Bayesian Inference?cited by 0