Multi-View Causal Representation Learning with Partial Observability

TL;DR

This paper introduces a theoretical framework for learning identifiable causal representations from multiple partially observed views using contrastive learning, extending previous work on multi-view nonlinear ICA and disentanglement.

Contribution

It provides a unified theoretical approach for identifying shared causal latent variables from partial views, including graphical criteria and a contrastive learning method.

Findings

Shared information across views can be learned up to a smooth bijection.

Graphical criteria determine which latent variables are identifiable.

Prior methods are recovered as special cases of this framework.

Abstract

We present a unified framework for studying the identifiability of representations learned from simultaneously observed views, such as different data modalities. We allow a partially observed setting in which each view constitutes a nonlinear mixture of a subset of underlying latent variables, which can be causally related. We prove that the information shared across all subsets of any number of views can be learned up to a smooth bijection using contrastive learning and a single encoder per view. We also provide graphical criteria indicating which latent variables can be identified through a simple set of rules, which we refer to as identifiability algebra. Our general framework and theoretical results unify and extend several previous works on multi-view nonlinear ICA, disentanglement, and causal representation learning. We experimentally validate our claims on numerical, image, and multi-modal data sets. Further, we demonstrate that the performance of prior methods is recovered in different special cases of our setup. Overall, we find that access to multiple partial views enables us to identify a more fine-grained representation, under the generally milder assumption of partial observability.