# Approximate Bayesian Computation via Classification

arXiv: https://arxiv.org/abs/2111.11507 · HTML: https://mlsanity.com/paper/2111.11507/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 78 references that are in the map.
- First posted on arXiv 22 Nov 2021.

## Builds on (most cited first, 19 of 19)

- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Posterior Concentration for Sparse Deep Learning](https://mlsanity.com/paper/1803.09138/) (2018)
- [Learning Summary Statistic for Approximate Bayesian Computation via Deep Neural Network](https://mlsanity.com/paper/1510.02175/) (2015)
- [Approximate Bayesian computation with the Wasserstein distance](https://mlsanity.com/paper/1905.03747/) (2019)
- [Robust Bayesian inference via coarsening](https://mlsanity.com/paper/1506.06101/) (2015)
- [Generalized Posteriors in Approximate Bayesian Computation](https://mlsanity.com/paper/2011.08644/) (2020)
- [Likelihood-free inference via classification](https://mlsanity.com/paper/1407.4981/) (2014)
- [Uncertainty Quantification for Sparse Deep Learning](https://mlsanity.com/paper/2002.11815/) (2020)
- [A Comparison of Likelihood-Free Methods With and Without Summary Statistics](https://mlsanity.com/paper/2103.02407/) (2021)
- [Convolutional Neural Networks as Summary Statistics for Approximate Bayesian Computation](https://mlsanity.com/paper/2001.11760/) (2020)
- [An Adversarial Approach to Structural Estimation](https://mlsanity.com/paper/2007.06169/) (2020)
- [Approximate Bayesian computation via the energy statistic](https://mlsanity.com/paper/1905.05884/) (2019)
- [Diagnosing model misspecification and performing generalized Bayes' updates via probabilistic classifiers](https://mlsanity.com/paper/1912.05810/) (2019)
- [Model Misspecification in ABC: Consequences and Diagnostics](https://mlsanity.com/paper/1708.01974/) (2017)
- [Generalised Bayes Updates with f-divergences through Probabilistic Classifiers](https://mlsanity.com/paper/2007.04358/) (2020)

## Built on by (most cited first, 2 of 2)

- [Generative Bayesian Inference with GANs](https://mlsanity.com/paper/2208.12113/) (2022)
- [Generative Bayesian Computation for Maximum Expected Utility](https://mlsanity.com/paper/2408.16101/) (2024)

## Abstract (arXiv)

Approximate Bayesian Computation (ABC) enables statistical inference in simulator-based models whose likelihoods are difficult to calculate but easy to simulate from. ABC constructs a kernel-type approximation to the posterior distribution through an accept/reject mechanism which compares summary statistics of real and simulated data. To obviate the need for summary statistics, we directly compare empirical distributions with a Kullback-Leibler (KL) divergence estimator obtained via contrastive learning. In particular, we blend flexible machine learning classifiers within ABC to automate fake/real data comparisons. We consider the traditional accept/reject kernel as well as an exponential weighting scheme which does not require the ABC acceptance threshold. Our theoretical results show that the rate at which our ABC posterior distributions concentrate around the true parameter depends on the estimation error of the classifier. We derive limiting posterior shape results and find that, with a properly scaled exponential kernel, asymptotic normality holds. We demonstrate the usefulness of our approach on simulated examples as well as real data in the context of stock volatility estimation.