# Posterior Matching for Arbitrary Conditioning

arXiv: https://arxiv.org/abs/2201.12414 · HTML: https://mlsanity.com/paper/2201.12414/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 41 references that are in the map.
- First posted on arXiv 28 Jan 2022.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [Variational Deep Embedding: An Unsupervised and Generative Approach to Clustering](https://mlsanity.com/paper/1611.05148/) (2016)
- [DRAW: A Recurrent Neural Network For Image Generation](https://mlsanity.com/paper/1502.04623/) (2015)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [EDDI: Efficient Dynamic Discovery of High-Value Information with Partial VAE](https://mlsanity.com/paper/1809.11142/) (2018)
- [Auxiliary Deep Generative Models](https://mlsanity.com/paper/1602.05473/) (2016)
- [Variational Autoencoder with Arbitrary Conditioning](https://mlsanity.com/paper/1806.02382/) (2018)
- [not-MIWAE: Deep Generative Modelling with Missing not at Random Data](https://mlsanity.com/paper/2006.12871/) (2020)
- [Active Feature Acquisition with Generative Surrogate Models](https://mlsanity.com/paper/2010.02433/) (2020)
- [Composing Normalizing Flows for Inverse Problems](https://mlsanity.com/paper/2002.11743/) (2020)
- [Latent Constraints: Learning to Generate Conditionally from Unconditional Generative Models](https://mlsanity.com/paper/1711.05772/) (2017)
- [Flow Models for Arbitrary Conditional Likelihoods](https://mlsanity.com/paper/1909.06319/) (2019)
- [VAEs in the Presence of Missing Data](https://mlsanity.com/paper/2006.05301/) (2020)
- [Autoregressive Energy Machines](https://mlsanity.com/paper/1904.05626/) (2019)
- [Arbitrary Conditional Distributions with Energy](https://mlsanity.com/paper/2102.04426/) (2021)
- [Learning about an exponential amount of conditional distributions](https://mlsanity.com/paper/1902.08401/) (2019)
- [A Universal Marginalizer for Amortized Inference in Generative Models](https://mlsanity.com/paper/1711.00695/) (2017)

## Built on by (most cited first, 4 of 4)

- [All-in-one simulation-based inference](https://mlsanity.com/paper/2404.09636/) (2024)
- [Learning to Receive Help: Intervention-Aware Concept Embedding Models](https://mlsanity.com/paper/2309.16928/) (2023)
- [Predictive World Models from Real-World Partial Observations](https://mlsanity.com/paper/2301.04783/) (2023)
- [Deeply-Learned Generalized Linear Models with Missing Data](https://mlsanity.com/paper/2207.08911/) (2022)

## Abstract (arXiv)

Arbitrary conditioning is an important problem in unsupervised learning, where we seek to model the conditional densities p(xu mid xo) that underly some data, for all possible non-intersecting subsets o, u subset 1, dots , d. However, the vast majority of density estimation only focuses on modeling the joint distribution p(x), in which important conditional dependencies between features are opaque. We propose a simple and general framework, coined Posterior Matching, that enables Variational Autoencoders (VAEs) to perform arbitrary conditioning, without modification to the VAE itself. Posterior Matching applies to the numerous existing VAE-based approaches to joint density estimation, thereby circumventing the specialized models required by previous approaches to arbitrary conditioning. We find that Posterior Matching is comparable or superior to current state-of-the-art methods for a variety of tasks with an assortment of VAEs (e.g.~discrete, hierarchical, VaDE).