# Variational Learning of Fractional Posteriors

Source: [Variational Learning of Fractional Posteriors](<https://www.sota2.com/research/paper/69cb555c0636e5bf4afca205>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-04-01T05:00:04.436Z

Authors: Kian Ming A. Chai, Edwin V. Bonilla

Published: 2026-03-29T02:55:35.000Z

## Abstract

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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Generative Modeling on Fashion MNIST (train)](<https://www.sota2.com/research/sota/generative-modeling-on-fashion-mnist-train.md>): Generative Modeling; Fashion-MNIST (train); Log Likelihood (100 samples): not recorded.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2603.27488>)

[PDF](<https://arxiv.org/pdf/2603.27488.pdf>)