The surprising strength of weak classifiers for validating neural posterior estimates

TL;DR

This paper demonstrates that weak classifiers, even if overfitted or biased, can reliably validate neural posterior estimates using a conformal C2ST method that controls Type-I error and maintains power.

Contribution

The authors introduce a conformal C2ST approach that converts any trained classifier's scores into valid p-values, enabling reliable validation of neural posterior estimates with weak classifiers.

Findings

Conformal C2ST controls Type-I error with finite samples.

Weak classifiers still provide powerful validation tests.

Empirical results outperform classical discriminative tests.

Abstract

Neural Posterior Estimation (NPE) has emerged as a powerful approach for amortized Bayesian inference when the true posterior $p(\theta \mid y)$ is intractable or difficult to sample. But evaluating the accuracy of neural posterior estimates remains challenging, with existing methods suffering from major limitations. One appealing and widely used method is the classifier two-sample test (C2ST), where a classifier is trained to distinguish samples from the true posterior $p(\theta \mid y)$ versus the learned NPE approximation $q(\theta \mid y)$. Yet despite the appealing simplicity of the C2ST, its theoretical and practical reliability depend upon having access to a near-Bayes-optimal classifier -- a requirement that is rarely met and, at best, difficult to verify. Thus a major open question is: can a weak classifier still be useful for neural posterior validation? We show that the answer is yes. Building on the work of Hu and Lei, we present several key results for a conformal variant of the C2ST, which converts any trained classifier's scores -- even those of weak or over-fitted models -- into exact finite-sample p-values. We establish two key theoretical properties of the conformal C2ST: (i) finite-sample Type-I error control, and (ii) non-trivial power that degrades gently in tandem with the error of the trained classifier. The upshot is that even weak, biased, or overfit classifiers can still yield powerful and reliable tests. Empirically, the Conformal C2ST outperforms classical discriminative tests across a wide range of benchmarks. These results reveal the under appreciated strength of weak classifiers for validating neural posterior estimates, establishing the conformal C2ST as a practical, theoretically grounded diagnostic for modern simulation-based inference.