Uncertainty Quantification for Prior-Data Fitted Networks using Martingale Posteriors

TL;DR

This paper introduces a new sampling method for uncertainty quantification in prior-data fitted networks, enabling Bayesian inference with proven convergence and demonstrated effectiveness.

Contribution

It proposes a martingale posterior-based sampling procedure for PFNs, providing a principled, efficient, and tuning-free approach to uncertainty quantification.

Findings

Method achieves well-calibrated uncertainty estimates.

Demonstrated efficiency on simulated and real-world datasets.

Proven convergence of the sampling procedure.

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.