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.

翻译：先验数据拟合网络（PFNs）已成为基于表格数据预测的通用基础模型，在小规模至中等规模数据集上无需调参即可达到先进性能。尽管PFNs受贝叶斯思想启发，但它们并未为预测均值、分位数或类似统计量提供任何不确定性量化。我们提出一种基于鞅后验的原则性、高效且免调参的采样程序，用于构建此类估计的贝叶斯后验分布，并证明了其收敛性。多个模拟与真实数据案例展示了该方法在推理应用中的效率与校准性能。