变分自编码器低质量数据生成原因剖析

Reasons for the Low Quality Data Generation of the Variation Auto-encoder

从数学角度对变分自编码器目标函数下界和网络结构进行了研究,指出变分自编码器所生成的样本质量低的两个原因:1)由于识别模型qφ(z|x)表达能力的限制使得后验分布pθ(z|x)偏离目标分布,导致最大化证据下限时没有能够保证最大化对数似然;2)变分自编码器中条件分布pθ(x|z)对应的网络结构把生成数据x和隐变量z之间的概率依赖关系近似为函数依赖关系,即把一个显示概率生成模型用一个隐式概率生成模型来近似实现。该结论为进一步研究和改进变分自编码器以及设计其他生成模型提供了理论支撑。

The lower bound of the objective function and the network structure of the variation auto-encoder are studied mathematically,and two reasons for the low quality data generated by the variation auto-encoder are analyzed as follows:1)Due to the limitation of the expression ability of the recognition model,the posterior distribution deviates from the target distribution,which results in the failure to ensure the maximum likelihood when maximizing the evidence lower bound;2)In the variation auto-encoder,the network structure of the conditional distribution approximates the probability dependency between generation data and implicit variable to a functional dependency,that is,an explicit probability generation model is approximated by an implicit probability model.These conclusions provide theoretical basis for further research and improvement of the variation auto-encoders and design of other generation models.