Identifiability of Cross-Domain Recommendation via Causal Subspace Disentanglement

Cross-Domain Recommendation~(CDR) seeks to enable effective knowledge transfer across domains. Most existing works rely on either representation alignment or transformation bridges, but they come with shortcomings regarding identifiability of domain-shared and domain-specific latent factors. Specifically, while CDR describes user representations as a joint distribution over two domains, these methods fail to account for its joint identifiability as they primarily fixate on the marginal distribution within a particular domain. Such a failure may overlook the conditionality between two domains and how it contributes to latent factor disentanglement, leading to negative transfer when domains are weakly correlated. In this study, we explore what should and should not be transferred in cross-domain user representations from a causality perspective. We propose a Hierarchical causal subspace disentanglement approach to explore the Joint IDentifiability of cross-domain joint distribution, termed HJID, to preserve domain-specific behaviors from domain-shared factors. HJID abides by the feature hierarchy and divides user representations into generic shallow subspace and domain-oriented deep subspaces. We first encode the generic pattern in the shallow subspace by minimizing the Maximum Mean Discrepancy of initial layer activation. Then, to dissect how domain-oriented latent factors are encoded in deeper layers activation, we construct a cross-domain causality-based data generation graph, which identifies cross-domain consistent and domain-specific components, adhering to the Minimal Change principle. This allows HJID to maintain stability whilst discovering unique factors for different domains, all within a generative framework of invertible transformations that guarantee the joint identifiability. With experiments on real-world datasets, we show that HJID outperforms SOTA methods on both strong- and weak-correlation CDR tasks.