  Learning predictors that do not rely on spurious correlations involves
building causal representations. However, learning such a representation is
very challenging. We, therefore, formulate the problem of learning a causal
representation from high dimensional data and study causal recovery with
synthetic data. This work introduces a latent variable decoder model, Decoder
BCD, for Bayesian causal discovery and performs experiments in mildly
supervised and unsupervised settings. We present a series of synthetic
experiments to characterize important factors for causal discovery and show
that using known intervention targets as labels helps in unsupervised Bayesian
inference over structure and parameters of linear Gaussian additive noise
latent structural causal models.
