# An efficient likelihood-free Bayesian inference method based on sequential neural posterior estimation

arXiv: https://arxiv.org/abs/2311.12530 · HTML: https://mlsanity.com/paper/2311.12530/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 61 references that are in the map.
- First posted on arXiv 21 Nov 2023.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [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)
- [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)
- [Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models](https://mlsanity.com/paper/1501.03291/) (2015)
- [Likelihood-free inference with emulator networks](https://mlsanity.com/paper/1805.09294/) (2018)
- [Mining gold from implicit models to improve likelihood-free inference](https://mlsanity.com/paper/1805.12244/) (2018)
- [Variational methods for simulation-based inference](https://mlsanity.com/paper/2203.04176/) (2022)
- [Truncated proposals for scalable and hassle-free simulation-based inference](https://mlsanity.com/paper/2210.04815/) (2022)
- [Bayesian Synthetic Likelihood](https://mlsanity.com/paper/2305.05120/) (2023)
- [A Trust Crisis In Simulation-Based Inference? Your Posterior Approximations Can Be Unfaithful](https://mlsanity.com/paper/2110.06581/) (2021)
- [Efficient acquisition rules for model-based approximate Bayesian computation](https://mlsanity.com/paper/1704.00520/) (2017)
- [Likelihood-free approximate Gibbs sampling](https://mlsanity.com/paper/1906.04347/) (2019)
- [Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-moments](https://mlsanity.com/paper/1603.01041/) (2016)
- [Modelling extremes using approximate Bayesian Computation](https://mlsanity.com/paper/1411.1451/) (2014)

## Abstract (arXiv)

Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from sequential simulation using neural network-based conditional density estimators by minimizing a specific loss function. The SNPE method proposed by Lueckmann et al. (2017) used a calibration kernel to boost the sample weights around the observed data, resulting in a concentrated loss function. However, the use of calibration kernels may increase the variances of both the empirical loss and its gradient, making the training inefficient. To improve the stability of SNPE, this paper proposes to use an adaptive calibration kernel and several variance reduction techniques. The proposed method greatly speeds up the process of training and provides a better approximation of the posterior than the original SNPE method and some existing competitors as confirmed by numerical experiments. We also managed to demonstrate the superiority of the proposed method for a high-dimensional model with a real-world dataset.