We propose a new supervised learning method for Variational AutoEncoder (VAE) which has a causally disentangled representation and achieves the causally disentangled generation (CDG) simultaneously. In this paper, CDG is defined as a generative model able to decode an output precisely according to the causally disentangled representation. We found that the supervised regularization of the encoder is not enough to obtain a generative model with CDG. Consequently, we explore sufficient and necessary conditions for the decoder and the causal effect to achieve CDG. Moreover, we propose a generalized metric measuring how a model is causally disentangled generative. Numerical results with the image and tabular datasets corroborate our arguments.

翻译：我们提出了一种新的变分自编码器（VAE）监督学习方法，该方法具有因果解耦表示，并同时实现了因果解耦生成（CDG）。在本文中，CDG被定义为一种能够根据因果解耦表示精确解码输出的生成模型。我们发现，编码器的监督正则化不足以获得具备CDG能力的生成模型。因此，我们探索了实现CDG所需的解码器与因果效应的充分必要条件。此外，我们提出了一种通用度量，用于衡量模型的因果解耦生成性能。基于图像和表格数据集的数值实验结果验证了我们的论点。