A principled framework for uncertainty decomposition in TabPFN

2026-02-04

AI Summary

This work addresses the lack of effective decomposition of aleatoric and epistemic uncertainty in TabPFN. It proposes the first principled framework for uncertainty decomposition by formulating the problem as Bayesian predictive inference. Epistemic uncertainty is estimated through the variability along the predictive update path, while aleatoric uncertainty is captured via entropy decomposition, enabling their separation in classification tasks. The method leverages the predictive central limit theorem under a quasi-martingale condition and employs an asymptotic surrogate of predictive Monte Carlo, ensuring computational efficiency without requiring retraining. The resulting credible intervals achieve near-nominal frequentist coverage, substantially improving the accuracy of epistemic uncertainty quantification.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

TabPFN is a transformer that achieves state-of-the-art performance on supervised tabular tasks by amortizing Bayesian prediction into a single forward pass. However, there is currently no method for uncertainty decomposition in TabPFN. Because it behaves, in an idealised limit, as a Bayesian in-context learner, we cast the decomposition challenge as a Bayesian predictive inference (BPI) problem. The main computational tool in BPI, predictive Monte Carlo, is challenging to apply here as it requires simulating unmodeled covariates. We therefore pursue the asymptotic alternative, filling a gap in the theory for supervised settings by proving a predictive CLT under quasi-martingale conditions. We derive variance estimators determined by the volatility of predictive updates along the context. The resulting credible bands are fast to compute, target epistemic uncertainty, and achieve near-nominal frequentist coverage. For classification, we further obtain an entropy-based uncertainty decomposition.

Problem

• uncertainty decomposition
• TabPFN
• Bayesian predictive inference
• epistemic uncertainty
• predictive uncertainty

Innovation

• uncertainty decomposition
• TabPFN
• Bayesian predictive inference
• predictive CLT
• epistemic uncertainty