C-Disentanglement: Discovering Causally-Independent Generative Factors under an Inductive Bias of Confounder

Representation learning assumes that real-world data is generated by a few causally disentangled generative factors (i.e., sources of variation). However, most existing works assume unconfoundedness (i.e., there are no common causes to the generative factors) in the discovery process, and thus obtain only statistical independence. In this paper, we recognize the importance of modeling confounders in discovering causal generative factors. Unfortunately, such factors are not identifiable without proper inductive bias. We fill the gap by introducing a framework named Confounded-Cisentanglement (C-Disentanglement), the first framework that explicitly introduces the inductive bias of confounder via labels/knowledge from domain expertise. We further propose an approach for sufficient identification under the VAE framework.