Inductive Domain Transfer In Misspecified Simulation-Based Inference

TL;DR

This paper introduces a fully inductive, end-to-end trainable SBI framework that improves scalability and robustness in misspecified models by integrating calibration and distribution alignment using optimal transport.

Contribution

It develops a novel amortized SBI method combining mini-batch optimal transport with a conditional normalizing flow, enabling efficient inference without test-time simulation.

Findings

Matches or surpasses RoPE and standard SBI methods in benchmarks

Improves scalability and applicability in misspecified environments

Effective on synthetic and real-world data, including medical biomarkers

Abstract

Simulation-based inference (SBI) is a statistical inference approach for estimating latent parameters of a physical system when the likelihood is intractable but simulations are available. In practice, SBI is often hindered by model misspecification--the mismatch between simulated and real-world observations caused by inherent modeling simplifications. RoPE, a recent SBI approach, addresses this challenge through a two-stage domain transfer process that combines semi-supervised calibration with optimal transport (OT)-based distribution alignment. However, RoPE operates in a fully transductive setting, requiring access to a batch of test samples at inference time, which limits scalability and generalization. We propose here a fully inductive and amortized SBI framework that integrates calibration and distributional alignment into a single, end-to-end trainable model. Our method leverages mini-batch OT with a closed-form coupling to align real and simulated observations that correspond to the same latent parameters, using both paired calibration data and unpaired samples. A conditional normalizing flow is then trained to approximate the OT-induced posterior, enabling efficient inference without simulation access at test time. Across a range of synthetic and real-world benchmarks--including complex medical biomarker estimation--our approach matches or surpasses the performance of RoPE, as well as other standard SBI and non-SBI estimators, while offering improved scalability and applicability in challenging, misspecified environments.