# CP4SBI: Local Conformal Calibration of Credible Sets in Simulation-Based Inference

arXiv: https://arxiv.org/abs/2508.17077 · HTML: https://mlsanity.com/paper/2508.17077/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 78 references that are in the map.
- First posted on arXiv 23 Aug 2025.

## Builds on (most cited first, 30 of 41)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [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)
- [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)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [CD-split and HPD-split: efficient conformal regions in high dimensions](https://mlsanity.com/paper/2007.12778/) (2020)
- [Flexible distribution-free conditional predictive bands using density estimators](https://mlsanity.com/paper/1910.05575/) (2019)
- [Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models](https://mlsanity.com/paper/1501.03291/) (2015)
- [Deep Learning in Bioinformatics](https://mlsanity.com/paper/1603.06430/) (2016)
- [Compositional Score Modeling for Simulation-based Inference](https://mlsanity.com/paper/2209.14249/) (2022)
- [Probabilistic Conformal Prediction Using Conditional Random Samples](https://mlsanity.com/paper/2206.06584/) (2022)
- [Truncated proposals for scalable and hassle-free simulation-based inference](https://mlsanity.com/paper/2210.04815/) (2022)
- [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)
- [Addressing Misspecification in Simulation-based Inference through Data-driven Calibration](https://mlsanity.com/paper/2405.08719/) (2024)
- [A Unified Comparative Study with Generalized Conformity Scores for Multi-Output Conformal Regression](https://mlsanity.com/paper/2501.10533/) (2025)
- [sbi reloaded: a toolkit for simulation-based inference workflows](https://mlsanity.com/paper/2411.17337/) (2024)
- [High-Dimensional Density Ratio Estimation with Extensions to Approximate Likelihood Computation](https://mlsanity.com/paper/1404.7063/) (2014)
- [HNPE: Leveraging Global Parameters for Neural Posterior Estimation](https://mlsanity.com/paper/2102.06477/) (2021)
- [Diffusion posterior sampling for simulation-based inference in tall data settings](https://mlsanity.com/paper/2404.07593/) (2024)
- [Confidence Sets and Hypothesis Testing in a Likelihood-Free Inference Setting](https://mlsanity.com/paper/2002.10399/) (2020)
- [L-C2ST: Local Diagnostics for Posterior Approximations in Simulation-Based Inference](https://mlsanity.com/paper/2306.03580/) (2023)

## Built on by (most cited first, 6 of 6)

- [Benchmarking Tabular Foundation Models for Conditional Density Estimation in Regression](https://mlsanity.com/paper/2603.26611/) (2026)
- [LoBoost: Fast Model-Native Local Conformal Prediction for Gradient-Boosted Trees](https://mlsanity.com/paper/2602.22432/) (2026)
- [LOCUS: A Distribution-Free Loss-Quantile Score for Risk-Aware Predictions](https://mlsanity.com/paper/2603.01971/) (2026)
- [CREDO: Epistemic-Aware Conformalized Credal Envelopes for Regression](https://mlsanity.com/paper/2603.06826/) (2026)
- [Conservative neural posterior estimation via distributionally robust training](https://mlsanity.com/paper/2605.28516/) (2026)
- [A Three-Way Testing Framework for Quantifying Epistemic Calibration Uncertainty in SBI](https://mlsanity.com/paper/2609.24419/) (2026)

## Abstract (arXiv)

Current experimental scientists have been increasingly relying on simulation-based inference (SBI) to invert complex non-linear models with intractable likelihoods. However, posterior approximations obtained with SBI are often miscalibrated, causing credible regions to undercover true parameters. We develop textttCP4SBI, a model-agnostic conformal calibration framework that constructs credible sets with local Bayesian coverage. Our two proposed variants, namely local calibration via regression trees and CDF-based calibration, enable finite-sample local coverage guarantees for any scoring function, including HPD, symmetric, and quantile-based regions. Experiments on widely used SBI benchmarks demonstrate that our approach improves the quality of uncertainty quantification for neural posterior estimators using both normalizing flows and score-diffusion modeling.