Learning Latent Structural Causal Models

TL;DR — Bayesian inference over latent structural causal models from low-level data under random, known interventions for linear Gaussian additive noise SCMs. Such a model also performs image generation from unseen interventions.

Abstract

Causal learning has long concerned itself with the recovery of underlying causal mechanisms. Such causal modelling enables better explanations of out-of-distribution data. Prior works on causal learning assume that the 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 latent and needs to be learnt from low-level data. We treat this problem as Bayesian inference of the latent SCM, given low-level data. We present BIOLS, a tractable approximate inference method which performs joint inference over the causal variables, structure and parameters of the latent SCM from known interventions. Experiments are performed on synthetic datasets and a causal benchmark image dataset to demonstrate the efficacy of our approach. We also demonstrate the ability of BIOLS to generate images from unseen interventional distributions.