L-C2ST: Local Diagnostics for Posterior Approximations in Simulation-Based Inference

TL;DR

L-C2ST is a new local diagnostic method for evaluating the trustworthiness of posterior approximations in simulation-based inference, providing interpretable, observation-specific assessments without needing true posterior samples.

Contribution

It introduces L-C2ST, a novel local evaluation technique for posterior estimators that enhances interpretability and efficiency, especially for normalizing flow-based models.

Findings

L-C2ST achieves comparable results to C2ST on benchmarks.

It outperforms alternative local evaluation methods like HPD coverage tests.

Demonstrates practical utility in computational neuroscience applications.

Abstract

Many recent works in simulation-based inference (SBI) rely on deep generative models to approximate complex, high-dimensional posterior distributions. However, evaluating whether or not these approximations can be trusted remains a challenge. Most approaches evaluate the posterior estimator only in expectation over the observation space. This limits their interpretability and is not sufficient to identify for which observations the approximation can be trusted or should be improved. Building upon the well-known classifier two-sample test (C2ST), we introduce L-C2ST, a new method that allows for a local evaluation of the posterior estimator at any given observation. It offers theoretically grounded and easy to interpret -- e.g. graphical -- diagnostics, and unlike C2ST, does not require access to samples from the true posterior. In the case of normalizing flow-based posterior estimators, L-C2ST can be specialized to offer better statistical power, while being computationally more efficient. On standard SBI benchmarks, L-C2ST provides comparable results to C2ST and outperforms alternative local approaches such as coverage tests based on highest predictive density (HPD). We further highlight the importance of local evaluation and the benefit of interpretability of L-C2ST on a challenging application from computational neuroscience.