We propose an adversarial training procedure for learning a causal implicit generative model for a given causal graph. We show that adversarial training can be used to learn a generative model with true observational and interventional distributions if the generator architecture is consistent with the given causal graph. We consider the application of generating faces based on given binary labels where the dependency structure between the labels is preserved with a causal graph. This problem can be seen as learning a causal implicit generative model for the image and labels. We devise a two-stage procedure for this problem. First we train a causal implicit generative model over binary labels using a neural network consistent with a causal graph as the generator. We empirically show that WassersteinGAN can be used to output discrete labels. Later, we propose two new conditional GAN architectures, which we call CausalGAN and CausalBEGAN. We show that the optimal generator of the CausalGAN, given the labels, samples from the image distributions conditioned on these labels. The conditional GAN combined with a trained causal implicit generative model for the labels is then a causal implicit generative model over the labels and the generated image. We show that the proposed architectures can be used to sample from observational and interventional image distributions, even for interventions which do not naturally occur in the dataset.
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