Beyond DAGs: A Latent Partial Causal Model for Multimodal Learning

Abstract: Directed acyclic graphs (DAGs) are fundamental graph structures in causal modeling, but identifying the desired DAG from observational data often requires strong assumptions that may not hold in real-world scenarios, especially for latent causal models and complex multimodal data. This raises the question of whether we can relax or bypass the DAG assumption while maintaining practical utility. In this work, we propose a novel latent partial causal model for multimodal data, featuring two latent coupled variables, connected by an undirected edge, to represent the transfer of knowledge across modalities. Under specific statistical assumptions, we establish an identifiability result, demonstrating that representations learned by multimodal contrastive learning correspond to the latent coupled variables up to a trivial transformation. This result deepens our understanding of the why multimodal contrastive learning works, highlights its potential for disentanglement, and expands the utility of pre-trained models like CLIP. Synthetic experiments confirm the robustness of our findings, even when the assumptions are partially violated. Most importantly, experiments on a pre-trained CLIP model embodies disentangled representations, enabling few-shot learning and improving domain generalization across diverse real-world datasets. Together, these contributions push the boundaries of multimodal contrastive learning, both theoretically and, crucially, in practical applications.