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 **U**nbiased, **U**nconfounding, and **U**nified **C**ausal **F**ramework (**U$^3$CF**) for MTDA. To *unify* align 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 induces 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.