Minimum Distance Summaries for Robust Neural Posterior Estimation

TL;DR

This paper introduces a robust neural posterior estimation method using minimum-distance summaries with MMD, enabling efficient, test-time adaptation that improves robustness to distributional misspecification in simulation-based inference.

Contribution

The authors propose a novel plug-in robust NPE approach using MMD-based summaries that adapt independently at test time, enhancing robustness without retraining the entire model.

Findings

Significant robustness improvements demonstrated on synthetic and real-world tasks.

Efficient implementation with random Fourier features for minimal overhead.

Theoretical guarantees established for robustness of the method.

Abstract

Simulation-based inference (SBI) enables amortized Bayesian inference by first training a neural posterior estimator (NPE) on prior-simulator pairs, typically through low-dimensional summary statistics, which can then be cheaply reused for fast inference by querying it on new test observations. Because NPE is estimated under the training data distribution, it is susceptible to misspecification when observations deviate from the training distribution. Many robust SBI approaches address this by modifying NPE training or introducing error models, coupling robustness to the inference network and compromising amortization and modularity. We introduce minimum-distance summaries, a plug-in robust NPE method that adapts queried test-time summaries independently of the pretrained NPE. Leveraging the maximum mean discrepancy (MMD) as a distance between observed data and a summary-conditional predictive distribution, the adapted summary inherits strong robustness properties from the MMD. We demonstrate that the algorithm can be implemented efficiently with random Fourier feature approximations, yielding a lightweight, model-free test-time adaptation procedure. We provide theoretical guarantees for the robustness of our algorithm and empirically evaluate it on a range of synthetic and real-world tasks, demonstrating substantial robustness gains with minimal additional overhead.