# Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability

arXiv: https://arxiv.org/abs/2310.13402 · HTML: https://mlsanity.com/paper/2310.13402/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 50 references that are in the map.
- First posted on arXiv 20 Oct 2023.

## Builds on (most cited first, 21 of 21)

- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Fast Differentiable Sorting and Ranking](https://mlsanity.com/paper/2002.08871/) (2020)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [The Emergence of Spectral Universality in Deep Networks](https://mlsanity.com/paper/1802.09979/) (2018)
- [Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models](https://mlsanity.com/paper/2210.04872/) (2022)
- [Sampling-Based Accuracy Testing of Posterior Estimators for General Inference](https://mlsanity.com/paper/2302.03026/) (2023)
- [Diagnostics for Conditional Density Models and Bayesian Inference Algorithms](https://mlsanity.com/paper/2102.10473/) (2021)
- [Towards Reliable Simulation-Based Inference with Balanced Neural Ratio Estimation](https://mlsanity.com/paper/2208.13624/) (2022)
- [Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flows](https://mlsanity.com/paper/2207.08219/) (2022)
- [Balancing Simulation-based Inference for Conservative Posteriors](https://mlsanity.com/paper/2304.10978/) (2023)
- [Validation Diagnostics for SBI algorithms based on Normalizing Flows](https://mlsanity.com/paper/2211.09602/) (2022)
- [Contrastive Neural Ratio Estimation for Simulation-based Inference](https://mlsanity.com/paper/2210.06170/) (2022)

## Built on by (most cited first, 11 of 11)

- [Addressing Misspecification in Simulation-based Inference through Data-driven Calibration](https://mlsanity.com/paper/2405.08719/) (2024)
- [Calibrating Bayesian Learning via Regularization, Confidence Minimization, and Selective Inference](https://mlsanity.com/paper/2404.11350/) (2024)
- [Low-Budget Simulation-Based Inference with Bayesian Neural Networks](https://mlsanity.com/paper/2408.15136/) (2024)
- [SOCIA-nabla: Textual Gradient Meets Multi-Agent Orchestration for Automated Simulator Generation](https://mlsanity.com/paper/2505.12006/) (2025)
- [A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarios](https://mlsanity.com/paper/2512.23748/) (2025)
- [Cost Estimation in Unit Commitment Problems Using Simulation-Based Inference](https://mlsanity.com/paper/2409.03588/) (2024)
- [Inherited or produced? Inferring protein production kinetics when protein counts are shaped by a cell's division history](https://mlsanity.com/paper/2506.09374/) (2025)
- [Conservative neural posterior estimation via distributionally robust training](https://mlsanity.com/paper/2605.28516/) (2026)
- [Fixed-Protocol Amortized MPS Tomography with Conformalized Predictive Uncertainty](https://mlsanity.com/paper/2607.11273/) (2026)
- [Mitigating Representation Gaps in Amortized Bayesian Inference with Auxiliary Supervision](https://mlsanity.com/paper/2609.39525/) (2026)
- [SLICE: Sequential Likelihood-Free Inference via Conformal E-Values](https://mlsanity.com/paper/2610.13855/) (2026)

## Abstract (arXiv)

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.