U$^3$CF: Unbiased, Unconfounding, and Unified Causal Framework for Multi-Target Domain Adaptation

Multi-target domain adaptation (MTDA) trains a model using a labeled source domain and several unlabeled target domains, aiming to enhance performance across all targets. However, existing methods lack a principled causal formulation and often rely on empirical domain-invariance enforcement, which can bias adaptation across targets. To fill this gap, we propose the Unbiased, Unconfounding, and Unified Causal Framework (U$^3$CF) for MTDA. To unify the alignment of multiple domains, we propose a prototype-driven alignment strategy that progressively updates prototypes by high-confidence target predictions, while the contrastive optimization objective jointly aligns target samples to semantic prototypes and preserves class discrimination. By formulating a structural causal model, we reveal that domain-invariant causal factors and domain-specific factors shape representations and labels, while the latter induce spurious label correlations across targets. Accordingly, U$^3$CF achieves unbiased prediction by disentangling representations into invariant causal components and domain-specific confounders and applying conditional intervention to block confounding effects while preserving invariant semantics. To ensure precise disentanglement, we leverage mutual information theory to derive a principled criterion for feature separation. Extensive experiments on four benchmarks demonstrate that U$^3$CF consistently outperforms leading methods.