# Balancing Simulation-based Inference for Conservative Posteriors

arXiv: https://arxiv.org/abs/2304.10978 · HTML: https://mlsanity.com/paper/2304.10978/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 21 Apr 2023.

## Builds on (most cited first, 20 of 20)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (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)
- [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)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation](https://mlsanity.com/paper/1605.06376/) (2016)
- [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)
- [Variational methods for simulation-based inference](https://mlsanity.com/paper/2203.04176/) (2022)
- [Truncated Marginal Neural Ratio Estimation](https://mlsanity.com/paper/2107.01214/) (2021)
- [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)
- [Confidence Sets and Hypothesis Testing in a Likelihood-Free Inference Setting](https://mlsanity.com/paper/2002.10399/) (2020)
- [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, 10 of 10)

- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability](https://mlsanity.com/paper/2310.13402/) (2023)
- [CP4SBI: Local Conformal Calibration of Credible Sets in Simulation-Based Inference](https://mlsanity.com/paper/2508.17077/) (2025)
- [Variational Inference with Coverage Guarantees in Simulation-Based Inference](https://mlsanity.com/paper/2305.14275/) (2023)
- [Low-Budget Simulation-Based Inference with Bayesian Neural Networks](https://mlsanity.com/paper/2408.15136/) (2024)
- [Simulation-based Inference with the Generalized Kullback-Leibler Divergence](https://mlsanity.com/paper/2310.01808/) (2023)
- [Cost Estimation in Unit Commitment Problems Using Simulation-Based Inference](https://mlsanity.com/paper/2409.03588/) (2024)
- [Conservative neural posterior estimation via distributionally robust training](https://mlsanity.com/paper/2605.28516/) (2026)
- [Bayesian Uncertainty Quantification for fMRI Functional Connectivity via Simulation-Based Inference](https://mlsanity.com/paper/2609.30445/) (2026)
- [Mitigating Representation Gaps in Amortized Bayesian Inference with Auxiliary Supervision](https://mlsanity.com/paper/2609.39525/) (2026)

## Abstract (arXiv)

Conservative inference is a major concern in simulation-based inference. It has been shown that commonly used algorithms can produce overconfident posterior approximations. Balancing has empirically proven to be an effective way to mitigate this issue. However, its application remains limited to neural ratio estimation. In this work, we extend balancing to any algorithm that provides a posterior density. In particular, we introduce a balanced version of both neural posterior estimation and contrastive neural ratio estimation. We show empirically that the balanced versions tend to produce conservative posterior approximations on a wide variety of benchmarks. In addition, we provide an alternative interpretation of the balancing condition in terms of the chi2 divergence.