# Neural Posterior Regularization for Likelihood-Free Inference

arXiv: https://arxiv.org/abs/2102.07770 · HTML: https://mlsanity.com/paper/2102.07770/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 23 references that are in the map.
- First posted on arXiv 15 Feb 2021.

## Builds on (most cited first, 17 of 17)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [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)
- [Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models](https://mlsanity.com/paper/1501.03291/) (2015)
- [Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation](https://mlsanity.com/paper/1605.06376/) (2016)
- [InfoMax-GAN: Improved Adversarial Image Generation via Information Maximization and Contrastive Learning](https://mlsanity.com/paper/2007.04589/) (2020)
- [Variational f-divergence Minimization](https://mlsanity.com/paper/1907.11891/) (2019)
- [Improved generator objectives for GANs](https://mlsanity.com/paper/1612.02780/) (2016)
- [Likelihood-Free Inference with Deep Gaussian Processes](https://mlsanity.com/paper/2006.10571/) (2020)
- [Adversarial Likelihood-Free Inference on Black-Box Generator](https://mlsanity.com/paper/2004.05803/) (2020)

## Abstract (arXiv)

A simulation is useful when the phenomenon of interest is either expensive to regenerate or irreproducible with the same context. Recently, Bayesian inference on the distribution of the simulation input parameter has been implemented sequentially to minimize the required simulation budget for the task of simulation validation to the real-world. However, the Bayesian inference is still challenging when the ground-truth posterior is multi-modal with a high-dimensional simulation output. This paper introduces a regularization technique, namely Neural Posterior Regularization (NPR), which enforces the model to explore the input parameter space effectively. Afterward, we provide the closed-form solution of the regularized optimization that enables analyzing the effect of the regularization. We empirically validate that NPR attains the statistically significant gain on benchmark performances for diverse simulation tasks.