提出一种新变分方法，可更准确估计分数后验并提升生成效果。
Variational Learning of Fractional Posteriors
- 基于单参数变分目标，直接逼近分数后验分布。
- 在混合模型和变分自编码器中实现更好校准与更高证据下界。
- 适合需要精准后验估计的生成建模任务，如图像生成。
我们提出一种新型单参数变分目标，用于下界估计数据证据，并实现近似分数后验的推断。该框架可扩展至层次化结构与贝叶斯后验，为概率建模提供通用工具。我们展示了两种可解析计算梯度的情形，并在混合模型上进行模拟研究，表明分数后验相比传统变分下界得到的后验具有更优校准性。应用于变分自编码器（VAEs）时，该方法获得更高的证据下界，同时联合学习高性能近似贝叶斯后验与分数后验。训练使用分数后验的VAE生成的解码器能更好地从先验中生成样本。
原文摘要 · Abstract (English)
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.
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