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

Problem
Simulation-based inference (SBI) often suffers from misspecification, where discrepancies between simulated and real-world observations arise due to modeling simplifications. Existing methods, such as RoPE, require ground-truth parameter calibration pairs, which are frequently unavailable in practical scenarios. This paper addresses the gap in the literature by proposing a novel approach that leverages unstructured side-channel information—such as regime labels and policy bulletins—to correct for misspecification without the need for calibration data. The work is presented as a preprint and has not undergone peer review.

Method
The authors propose Misspecification-Aware Simulation-Based Inference (MA-SBI), a framework that utilizes a learned corrector to map side-channel text to an observation-space shift. This shift is applied prior to any pre-trained amortized posterior, allowing for bias correction without retraining or requiring parameter ground-truth. The theoretical foundation includes a main theorem that establishes bounds on achievable bias reduction, which is contingent on the mutual information between the misspecification and the side-channel data. The framework is designed to handle sub-Gaussian noise through the Donsker-Varadhan theorem. The authors also introduce a stochastic variant of MA-SBI that enhances posterior-predictive log-likelihood.

Results
MA-SBI demonstrates strong performance on hide-the-calibration benchmarks, achieving TOST equivalence with the oracle posterior across 10 seeds and two backbone architectures when using text alone. In contrast, RoPE, which relies on more data, does not achieve the same level of performance. Additionally, the stochastic variant of MA-SBI shows improved posterior-predictive log-likelihood on real-world datasets, including COVID and OxCGRT epidemiological data, while maintaining the posterior on a well-specified cognitive-science corpus.

Limitations
The authors acknowledge that MA-SBI’s performance is contingent on the quality and relevance of the side-channel information. If the side-channel data is poorly aligned with the misspecification, the effectiveness of the correction may diminish. Furthermore, the theoretical bounds provided may not account for all forms of noise or misspecification, potentially limiting the generalizability of the results. The paper does not explore the computational complexity of the learned corrector or the scalability of the approach in high-dimensional settings.

Why it matters
MA-SBI represents a significant advancement in SBI by enabling practitioners to utilize readily available side-channel information for bias correction, thus broadening the applicability of SBI in real-world scenarios where calibration data is scarce. This work has implications for various fields, including epidemiology and cognitive science, where accurate inference from simulations is critical. The findings contribute to the ongoing discourse on improving SBI methodologies, as discussed in related literature, and are available on arXiv.