Prior-data fitted networks (PFNs) have emerged as promising foundation models for prediction from tabular data sets, 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 and efficient 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 uncertainty quantification of our method in inference applications.

翻译：先验数据拟合网络（PFNs）已成为表格数据集预测领域有前景的基础模型，在无需调参的情况下于中小规模数据上实现了最先进的性能。虽然PFNs的设计受到贝叶斯思想的启发，但其未能为预测均值、分位数或类似统计量提供不确定性量化。本文提出一种基于鞅后验的严谨高效采样方法，用于构建此类估计量的贝叶斯后验分布，并证明其收敛性。通过多个模拟与真实数据案例，展示了该方法在统计推断应用中的不确定性量化能力。