  Causal learning has long concerned itself with the accurate recovery of
underlying causal mechanisms. Such causal modelling enables better explanations
of out-of-distribution data. Prior works on causal learning assume that the
high-level causal variables are given. However, in machine learning tasks, one
often operates on low-level data like image pixels or high-dimensional vectors.
In such settings, the entire Structural Causal Model (SCM) -- structure,
parameters, \textit{and} high-level causal variables -- is unobserved and needs
to be learnt from low-level data. We treat this problem as Bayesian inference
of the latent SCM, given low-level data. For linear Gaussian additive noise
SCMs, we present a tractable approximate inference method which performs joint
inference over the causal variables, structure and parameters of the latent SCM
from random, known interventions. Experiments are performed on synthetic
datasets and a causally generated image dataset to demonstrate the efficacy of
our approach. We also perform image generation from unseen interventions,
thereby verifying out of distribution generalization for the proposed causal
model.
