解决跨域推荐中的分布偏移问题，提升模型在真实场景下的泛化能力。

Cross-Domain Recommendation (CDR) aims to leverage knowledge from a relatively data-richer source domain to address the data sparsity problem in a relatively data-sparser target domain. While CDR methods need to address the distribution shifts between different domains, i.e., cross-domain distribution shifts (CDDS), they typically assume independent and identical distribution (IID) between training and testing data within the target domain. However, this IID assumption rarely holds in real-world scenarios due to single-domain distribution shift (SDDS). The above two co-existing distribution shifts lead to out-of-distribution (OOD) environments that hinder effective knowledge transfer and generalization, ultimately degrading recommendation performance in CDR. To address these co-existing distribution shifts, we propose a novel Causal-Invariant Cross-Domain Out-of-distribution Recommendation framework, called CICDOR. In CICDOR, we first learn dual-level causal structures to infer domain-specific and domain-shared causal-invariant user preferences for tackling both CDDS and SDDS under OOD environments in CDR. Then, we propose an LLM-guided confounder discovery module that seamlessly integrates LLMs with a conventional causal discovery method to extract observed confounders for effective deconfounding, thereby enabling accurate causal-invariant preference inference. Extensive experiments on two real-world datasets demonstrate the superior recommendation accuracy of CICDOR over state-of-the-art methods across various OOD scenarios.