Uncertainty Quantification for Prior-Data Fitted Networks using Martingale Posteriors

2025/05/16 by Thomas Nägler, David Rügamer, Nagler, Thomas +1 · 1 citation
Decision Sciences · Engineering · #Artificial Intelligence (cs.AI) #Computation (stat.CO) #FOS: Computer and information sciences #Fault Detection and Control Systems #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME) #Probabilistic and Robust Engineering Design #Reliability and Maintenance Optimization

paper · pdf · doi:10.48550/arxiv.2505.11325

openalex publication_date 2025/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• TabICLv2: A better, faster, scalable, and open tabular foundation model
• Uncertainty Decomposition for Bayes-Filtered Transformers via Bayesian Predictive Inference
• TabMGP: Martingale Posterior with TabPFN
• TabICL: A Tabular Foundation Model for In-Context Learning on Large Data
• TabPFN Unleashed: A Scalable and Effective Solution to Tabular Classification Problems
• Can Transformers Learn Full Bayesian Inference in Context?
• Quasi-Bayes meets Vines
• Retrieval & Fine-Tuning for In-Context Tabular Models
• Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspective
• TuneTables: Context Optimization for Scalable Prior-Data Fitted Networks
• What Can Transformers Learn In-Context? A Case Study of Simple Function Classes
• TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second
• Transformers Can Do Bayesian Inference
• Martingale posterior distributions
• Subspace Inference for Bayesian Deep Learning
• Time-uniform Chernoff bounds via nonnegative supermartingales
• Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles
• Limit theorems for a class of identically distributed random variables
• Modeling of strength of high-performance concrete using artificial neural networks

Cited by

• TabMGP: Martingale Posterior with TabPFN

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