论文标题
基于指数分散族的$β$变量自动编码器的广义线性模型框架
A Generalised Linear Model Framework for $β$-Variational Autoencoders based on Exponential Dispersion Families
论文作者
论文摘要
尽管差异自动编码器（VAE）成功地用于获得高维数据的有意义的低维表示，但尚未完全了解一般观察模型的损失函数临界点的表征。我们引入了一个理论框架，该框架基于$β$ -VAE与广义线性模型（GLM）之间的连接。基于观察模型分布属于指数分散族（EDF）的假设，$β$ -VAE的激活函数与GLM链接函数的逆逆函数之间的平等使我们能够对$β$ -VAE的损失分析进行系统的概括。结果，我们可以根据最大似然估计（MLE）初始化$β$ -VAE网络，从而提高合成和现实世界数据集的训练性能。进一步的结果，我们分析描述了$β$ -VAE目标固有的自动修复特性和后倒塌的原因。
Although variational autoencoders (VAE) are successfully used to obtain meaningful low-dimensional representations for high-dimensional data, the characterization of critical points of the loss function for general observation models is not fully understood. We introduce a theoretical framework that is based on a connection between $β$-VAE and generalized linear models (GLM). The equality between the activation function of a $β$-VAE and the inverse of the link function of a GLM enables us to provide a systematic generalization of the loss analysis for $β$-VAE based on the assumption that the observation model distribution belongs to an exponential dispersion family (EDF). As a result, we can initialize $β$-VAE nets by maximum likelihood estimates (MLE) that enhance the training performance on both synthetic and real world data sets. As a further consequence, we analytically describe the auto-pruning property inherent in the $β$-VAE objective and reason for posterior collapse.
