# Variational Learning of Fractional Posteriors

arXiv: https://arxiv.org/abs/2603.27488 · HTML: https://mlsanity.com/paper/2603.27488/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 51 references that are in the map.
- First posted on arXiv 29 Mar 2026.

## Builds on (most cited first, 27 of 27)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [On the properties of variational approximations of Gibbs posteriors](https://mlsanity.com/paper/1506.04091/) (2015)
- [R'enyi Divergence Variational Inference](https://mlsanity.com/paper/1602.02311/) (2016)
- [An Introduction to Deep Generative Modeling](https://mlsanity.com/paper/2103.05180/) (2021)
- [Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference](https://mlsanity.com/paper/1703.09194/) (2017)
- [Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It](https://mlsanity.com/paper/1412.3730/) (2014)
- [Hierarchical Variational Models](https://mlsanity.com/paper/1511.02386/) (2015)
- [Posterior Collapse and Latent Variable Non-identifiability](https://mlsanity.com/paper/2301.00537/) (2023)
- [Semi-Implicit Variational Inference](https://mlsanity.com/paper/1805.11183/) (2018)
- [Importance Weighting and Variational Inference](https://mlsanity.com/paper/1808.09034/) (2018)
- [Yes, but Did It Work?: Evaluating Variational Inference](https://mlsanity.com/paper/1802.02538/) (2018)
- [The continuous Bernoulli: fixing a pervasive error in variational autoencoders](https://mlsanity.com/paper/1907.06845/) (2019)
- [Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequences](https://mlsanity.com/paper/1609.00978/) (2016)
- [Unbiased Implicit Variational Inference](https://mlsanity.com/paper/1808.02078/) (2018)
- [Robust Bayesian inference via coarsening](https://mlsanity.com/paper/1506.06101/) (2015)
- [Calibrating general posterior credible regions](https://mlsanity.com/paper/1509.00922/) (2015)
- [PACm-Bayes: Narrowing the Empirical Risk Gap in the Misspecified Bayesian Regime](https://mlsanity.com/paper/2010.09629/) (2020)
- [On the Robustness to Misspecification of α-Posteriors and Their Variational Approximations](https://mlsanity.com/paper/2104.08324/) (2021)
- [Model Selection for Bayesian Autoencoders](https://mlsanity.com/paper/2106.06245/) (2021)
- [Implicit Variational Inference for High-Dimensional Posteriors](https://mlsanity.com/paper/2310.06643/) (2023)
- [On the use of bootstrap with variational inference: Theory, interpretation, and a two-sample test example](https://mlsanity.com/paper/1711.11057/) (2017)
- [The fine print on tempered posteriors](https://mlsanity.com/paper/2309.05292/) (2023)

## Abstract (arXiv)

We introduce a novel one-parameter variational objective that lower bounds the data evidence and enables the estimation of approximate fractional posteriors. We extend this framework to hierarchical construction and Bayes posteriors, offering a versatile tool for probabilistic modelling. We demonstrate two cases where gradients can be obtained analytically and a simulation study on mixture models showing that our fractional posteriors can be used to achieve better calibration compared to posteriors from the conventional variational bound. When applied to variational autoencoders (VAEs), our approach attains higher evidence bounds and enables learning of high-performing approximate Bayes posteriors jointly with fractional posteriors. We show that VAEs trained with fractional posteriors produce decoders that are better aligned for generation from the prior.