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

Antoine Wehenkel, Juan L. Gamella, Ozan Sener, Jens Behrmann, Guillermo Sapiro, marco cuturi, Joern-Henrik Jacobsen

Keywords: Simulation-based inference, SBI, Bayesian Inference, Misspecification, Likelihood-free, Robust Inference, Physics-informed Machine Learning

TL;DR: We introduce ROPE a simulation-based inference algorithm that relies on Neural Posterior Estimation and Optimal Transport to handle model misspecification with a small calibration set.

Abstract:

Driven by steady progress in generative modeling, simulation-based inference (SBI) has enabled inference over stochastic simulators. However, recent work has demonstrated that model misspecification can harm SBI's reliability, 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 problem between learned representations of real-world and simulated observations, allowing the method to learn a model of the misspecification without placing additional assumptions on its nature. The method shows how a small calibration set can be leveraged to offer a controllable balance between calibrated uncertainty and informative inference even under severely misspecified simulators. Our empirical 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.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 3687