Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability

Published: 21 Sept 2023, Last Modified: 15 Jan 2024NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: simulation-based inference, inverse problem, bayesian inference, uncertainty quantification, generative modeling
TL;DR: Regularization method for neural simulation-based inference that uses a differentiable computation of posterior's expected coverage probability.
Abstract: Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a simulator posing the need for simulation-based inference (SBI). However, the existing algorithms can yield overconfident posteriors (Hermans *et al.*, 2022) defeating the whole purpose of credibility if the uncertainty quantification is inaccurate. We propose to include a calibration term directly into the training objective of the neural model in selected amortized SBI techniques. By introducing a relaxation of the classical formulation of calibration error we enable end-to-end backpropagation. The proposed method is not tied to any particular neural model and brings moderate computational overhead compared to the profits it introduces. It is directly applicable to existing computational pipelines allowing reliable black-box posterior inference. We empirically show on six benchmark problems that the proposed method achieves competitive or better results in terms of coverage and expected posterior density than the previously existing approaches.
Supplementary Material: zip
Submission Number: 4628