MA-SBI: Misspecification-Aware Simulation-Based Inference via Side-Channel Guidance

2026-06-15

AI Summary

This work addresses model misspecification in simulation-based inference arising from simplifying assumptions, particularly when ground-truth parameter–observation pairs are unavailable. It introduces the first calibration-free posterior correction framework that leverages unstructured side-channel information—such as textual labels or policy announcements—to learn a mapping from such auxiliary signals to shifts in observation space. Without retraining the simulator or requiring access to true parameters, the method enhances inference robustness. Theoretically, the correction efficacy is bounded by the mutual information between model misspecification and the side channel. Empirically, on a hidden benchmark, textual side information alone yields a posterior statistically equivalent to the oracle (validated via TOST), outperforming RoPE despite using less data. The approach also significantly improves predictive log-likelihood on real-world COVID/OxCGRT data while preserving posterior consistency in well-specified cognitive science tasks.

Abstract

Simulation-based inference (SBI) of latent parameters is often hindered by simulator misspecification, the mismatch between simulated and real-world observations caused by inherent modeling simplifications. RoPE, the recent state-of-the-art for robust SBI, addresses this through optimal transport between learned representations of real and simulated observations, but requires ground-truth parameter calibration pairs that are typically unavailable in the very settings where SBI is needed. What practitioners do have is unstructured side-information such as regime labels, instruction text, and policy bulletins. We propose Misspecification-Aware Simulation-Based Inference (MA-SBI), a calibration-free framework that turns this side-channel into a posterior correction. A learned corrector maps side-channel text to an observation-space shift applied before any pre-trained amortized posterior, requiring no retraining and no parameter ground-truth. Our main theorem bounds achievable bias reduction by the mutual information between misspecification and side-channel, with a non-vacuous constant that extends to all sub-Gaussian noise via Donsker-Varadhan. On hide-the-calibration benchmarks, MA-SBI with text alone matches the oracle posterior across 10 seeds and two backbones (TOST equivalence), while RoPE given more data does not. The two approaches are complementary: where misspecification is structural and recoverable from parameter pairs, RoPE dominates, as the theory predicts. A stochastic variant improves posterior-predictive log-likelihood on real COVID and OxCGRT epidemiological data, and correctly leaves the posterior unchanged on a well-specified cognitive-science corpus.

Problem

• simulator misspecification
• simulation-based inference
• side-channel information
• posterior correction
• calibration-free

Innovation

• simulation-based inference
• simulator misspecification
• side-channel guidance
• posterior correction
• calibration-free