Conservative neural posterior estimation via distributionally robust training

2026-05-27

AI Summary

This work addresses the issue of overconfident and unreliable posterior distributions commonly produced by Neural Posterior Estimation (NPE) under limited simulation budgets. To mitigate this, the authors propose DRO-NPE, a distributionally robust optimization framework that replaces the standard NPE objective with a worst-case loss over a Wasserstein ambiguity set. The method integrates normalizing flows with a parallel training strategy and introduces KL divergence–based metrics to quantify under-coverage and calibration error, effectively curbing overfitting and overconfidence. Experimental results demonstrate that DRO-NPE significantly improves posterior coverage and calibration across multiple simulation-based inference benchmarks, narrows the gap between empirical and population losses, and yields more reliable Bayesian inference—particularly in low-simulation regimes.

Abstract

Simulation-based inference with neural posterior estimation (NPE) often yields overconfident and unreliable posteriors under limited simulation budgets. To address this, we propose DRO-NPE, a distributionally robust approach that replaces the standard NPE objective with a worst-case loss over a Wasserstein ambiguity set. We introduce KL-based metrics for miscoverage and miscalibration, and use these to show that the DRO-NPE objective controls overfitting and reduces posterior overconfidence. Our method is tractable, parallelisable, and readily integrates with standard normalising flows. Across benchmark SBI tasks, DRO-NPE consistently improves coverage and calibration, while narrowing the gap between empirical and population NPE loss, leading to more reliable inference in low-simulation regimes.

Problem

• simulation-based inference
• neural posterior estimation
• overconfidence
• limited simulation budget
• posterior reliability

Innovation

• distributionally robust optimization
• neural posterior estimation
• Wasserstein ambiguity set
• simulation-based inference
• posterior calibration