Addressing Misspecification in Simulation-based Inference through Data-driven Calibration

TL;DR

This paper introduces RoPE, a robust framework for simulation-based inference that uses optimal transport and real-world calibration data to address model misspecification, improving the reliability of parameter estimation.

Contribution

RoPE is a novel method that leverages optimal transport and calibration data to correct for model misspecification in SBI without additional assumptions.

Findings

RoPE outperforms baseline methods on synthetic and real-world tasks.

RoPE provides calibrated credible intervals even with severely misspecified models.

The framework balances uncertainty and informativeness through OT and calibration data.

Abstract

Driven by steady progress in deep generative modeling, simulation-based inference (SBI) has emerged as the workhorse for inferring the parameters of stochastic simulators. However, recent work has demonstrated that model misspecification can compromise the reliability of SBI, preventing its adoption in important applications where only misspecified simulators are available. This work introduces robust posterior estimation~(RoPE), a framework that overcomes model misspecification with a small real-world calibration set of ground-truth parameter measurements. We formalize the misspecification gap as the solution of an optimal transport~(OT) problem between learned representations of real-world and simulated observations, allowing RoPE to learn a model of the misspecification without placing additional assumptions on its nature. RoPE demonstrates how OT and a calibration set provide a controllable balance between calibrated uncertainty and informative inference, even under severely misspecified simulators. Results on four synthetic tasks and two real-world problems with ground-truth labels demonstrate that RoPE outperforms baselines and consistently returns informative and calibrated credible intervals.