Multi-View Causal Representation Learning with Partial Observability

2023/11/07 by Dingling Yao, Yao, Dingling, Danru Xu +13 · 21 citations
Computer Science · Mathematics · #Adversarial Robustness in Machine Learning #Algorithm #Applied mathematics #Artificial Intelligence (cs.AI) #Artificial intelligence #Bijection #Computer science #Discrete mathematics #Domain Adaptation and Few-Shot Learning #Encoder #Explainable Artificial Intelligence (XAI) #FOS: Computer and information sciences #Feature learning #Identifiability #Latent variable #Machine Learning (cs.LG) #Machine learning #Mathematics #Nonlinear system #Observability #Representation (politics) #Set (abstract data type) #Simple (philosophy) #Theoretical computer science #Tuple

paper · pdf · doi:10.48550/arxiv.2311.04056

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2023/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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