Learning Robust Statistics for Simulation-based Inference under Model Misspecification

Daolang Huang, Ayush Bharti, Amauri H Souza, Luigi Acerbi, Samuel Kaski

Keywords: Simulation-based inference, model misspecification, likelihood-free inference, approximate Bayesian computation, neural posterior estimation

TL;DR: We introduce the first general approach for tackling model misspecification in simulation-based inference that relies on learning robust statistics.

Abstract: Simulation-based inference (SBI) methods such as approximate Bayesian computation (ABC), synthetic likelihood, and neural posterior estimation (NPE) rely on simulating statistics to infer parameters of intractable likelihood models. However, such methods are known to yield untrustworthy and misleading inference outcomes under model misspecification, thus hindering their widespread applicability. In this work, we propose the first general approach to handle model misspecification that works across different classes of SBI methods. Leveraging the fact that the choice of statistics determines the degree of misspecification in SBI, we introduce a regularized loss function that penalizes those statistics that increase the mismatch between the data and the model. Taking NPE and ABC as use cases, we demonstrate the superior performance of our method on high-dimensional time-series models that are artificially misspecified. We also apply our method to real data from the field of radio propagation where the model is known to be misspecified. We show empirically that the method yields robust inference in misspecified scenarios, whilst still being accurate when the model is well-specified.

Submission Number: 1632