Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability
This addresses the need for reliable uncertainty quantification in Bayesian inference for researchers using SBI, though it is incremental as it builds on existing amortized SBI techniques.
The paper tackles the problem of overconfident posteriors in simulation-based inference (SBI) by proposing a calibration term integrated into the training objective of neural models, enabling end-to-end backpropagation. It shows competitive or better results in coverage and expected posterior density on six benchmark problems.
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.