Distributional Regression with Tabular Foundation Models: Evaluating Probabilistic Predictions via Proper Scoring Rules

Abstract

Tabular foundation models such as TabPFN and TabICL already produce full predictive distributions, yet the benchmarks used to evaluate them (TabArena, TALENT, and others) still rely almost exclusively on point-estimate metrics (RMSE, $R^2$). This mismatch implicitly rewards models that elicit a good conditional mean while ignoring the quality of the predicted distribution. We make two contributions. First, we propose supplementing standard point metrics with proper scoring rules (CRPS, CRLS, and the Interval Score) and provide a head-to-head comparison of realTabPFNv2.5 and TabICLv2 with regards to some proper scoring rules across 20 OpenML regression datasets. Second, we show analytically and empirically that different proper scoring rules induce different model rankings and different inductive biases during training, even though each rule is individually minimized by the true distribution. Fine-tuning realTabPFNv2.5 with scoring rules not seen during pretraining (CRLS, $β=1.8$ energy score) yields consistent improvements on the corresponding metrics, confirming that the training loss shapes the model beyond what propriety alone guarantees. Together, these findings argue for (i) reporting distributional metrics in tabular regression benchmarks and (ii) making the training objective of foundation models adaptable (via fine-tuning or task-token conditioning) to the scoring rule relevant to the downstream decision problem.