Uncertainty Quantification for Prior-Data Fitted Networks using Martingale Posteriors

Thomas Nagler; David Rügamer

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arXiv · 2505.11325

Uncertainty Quantification for Prior-Data Fitted Networks using Martingale Posteriors

Thomas Nagler·David Rügamer

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Abstract

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.

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Thomas Nagler, David Rügamer. 2025-05-16. Uncertainty Quantification for Prior-Data Fitted Networks using Martingale Posteriors. https://arxiv.org/abs/2505.11325

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