IWCAE: Importance-Weighted Conditional Autoencoders for Domain-Adaptive Generative Modeling

Generative models characterize full data distributions and support a broad range of downstream tasks, but their performance may deteriorate when the training and testing distributions differ. Existing domain adaptation methods are often developed under covariate shift or label shift assumptions, which may be restrictive under substantial domain shift. We instead consider a more flexible setting in which there exists a representation under which the conditional response distribution is invariant across domains. We propose an importance-weighted conditional variational autoencoder, termed IWCAE, for transferable conditional distribution learning. IWCAE learns the full conditional response distribution through an importance-weighted conditional likelihood objective while using a maximum mean discrepancy penalty to align the marginal representation distributions across the training and testing domains. This design seeks to preserve predictive information while suppressing domain-specific variation. We further develop a sampling-importance-resampling procedure for approximate predictive sampling when direct sampling from the conditional latent prior is difficult. Theoretically, we establish the asymptotic validity of the proposed sampling procedure. Experiments on three medical datasets demonstrate the effectiveness of IWCAE in improving cross-domain predictive performance and quantifying predictive uncertainty under distribution shift.