Causally Disentangled Generative Variational AutoEncoder

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.