# Amortized Bayesian Mixture Models

arXiv: https://arxiv.org/abs/2501.10229 · HTML: https://mlsanity.com/paper/2501.10229/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 104 references that are in the map.
- First posted on arXiv 17 Jan 2025.

## Builds on (most cited first, 30 of 40)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [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)
- [Population Based Training of Neural Networks](https://mlsanity.com/paper/1711.09846/) (2017)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Sensitivity and Generalization in Neural Networks: an Empirical Study](https://mlsanity.com/paper/1802.08760/) (2018)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC](https://mlsanity.com/paper/1507.04544/) (2015)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [Mining gold from implicit models to improve likelihood-free inference](https://mlsanity.com/paper/1805.12244/) (2018)
- [Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models](https://mlsanity.com/paper/2210.04872/) (2022)
- [Bayesian Workflow](https://mlsanity.com/paper/2011.01808/) (2020)
- [Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks](https://mlsanity.com/paper/2112.08866/) (2021)
- [Pareto Smoothed Importance Sampling](https://mlsanity.com/paper/1507.02646/) (2015)
- [Visualization in Bayesian workflow](https://mlsanity.com/paper/1709.01449/) (2017)
- [Deep Amortized Inference for Probabilistic Programs](https://mlsanity.com/paper/1610.05735/) (2016)
- [Consistency Models for Scalable and Fast Simulation-Based Inference](https://mlsanity.com/paper/2312.05440/) (2023)
- [Mixture models with a prior on the number of components](https://mlsanity.com/paper/1502.06241/) (2015)
- [Sensitivity-Aware Amortized Bayesian Inference](https://mlsanity.com/paper/2310.11122/) (2023)
- [Simulation-Based Calibration Checking for Bayesian Computation: The Choice of Test Quantities Shapes Sensitivity](https://mlsanity.com/paper/2211.02383/) (2022)
- [Toward a principled Bayesian workflow in cognitive science](https://mlsanity.com/paper/1904.12765/) (2019)

## Built on by (most cited first, 3 of 3)

- [Diffusion Models in Simulation-Based Inference: A Tutorial Review](https://mlsanity.com/paper/2512.20685/) (2025)
- [BayesFlow 2: Multi-Backend Amortized Bayesian Inference in Python](https://mlsanity.com/paper/2602.07098/) (2026)
- [Amortized Bayesian Inference on Multilevel Models of Arbitrary Structure](https://mlsanity.com/paper/2609.40024/) (2026)

## Abstract (arXiv)

Finite mixtures are a broad class of models useful in scenarios where observed data is generated by multiple distinct processes but without explicit information about the responsible process for each data point. Estimating Bayesian mixture models is computationally challenging due to issues such as high-dimensional posterior inference and label switching. Furthermore, traditional methods such as MCMC are applicable only if the likelihoods for each mixture component are analytically tractable. Amortized Bayesian Inference (ABI) is a simulation-based framework for estimating Bayesian models using generative neural networks. This allows the fitting of models without explicit likelihoods, and provides fast inference. ABI is therefore an attractive framework for estimating mixture models. This paper introduces a novel extension of ABI tailored to mixture models. We factorize the posterior into a distribution of the parameters and a distribution of (categorical) mixture indicators, which allows us to use a combination of generative neural networks for parameter inference, and classification networks for mixture membership identification. The proposed framework accommodates both independent and dependent mixture models, enabling filtering and smoothing. We validate and demonstrate our approach through synthetic and real-world datasets.