Valid Feature-Level Inference for Tabular Foundation Models via the Conditional Randomization Test
Abstract
Modern machine learning models are highly expressive but notoriously difficult to analyze statistically. In particular, while black-box predictors can achieve strong empirical performance, they rarely provide valid hypothesis tests or p-values for assessing whether individual features contain information about a target variable. This article presents a practical approach to feature-level hypothesis testing that combines the Conditional Randomization Test (CRT) with TabPFN, a probabilistic foundation model for tabular data. The resulting procedure yields finite-sample valid p-values for conditional feature relevance, even in nonlinear and correlated settings, without requiring model retraining or parametric assumptions.
Figures & tables
| Dataset | Power | Type-I Error | ||
|---|---|---|---|---|
| Linear (sparse) | 10 | 3 | 1.00 | 0.03 |
| Linear (dense) | 5 | 5 | 1.00 | 0.00 |
| Weak signal | 5 | 2 | 1.00 | 0.07 |
| Noise block | 20 | 2 | 1.00 | 0.03 |
| Correlated linear | 5 | 1 | 1.00 | 0.10 |
| Friedman 1 | 10 | 5 | 1.00 | 0.04 |
Statistical Hypothesis Testing
Statistical hypothesis testing develops methods for assessing evidence against a stated null while controlling false-positive and false-negative rates.
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