Spatial Variational Auto-Encoding via Matrix-Variate Normal Distributions

The key idea of variational auto-encoders (VAEs) resembles that of traditional auto-encoder models in which spatial information is supposed to be explicitly encoded in the latent space. However, the latent variables in VAEs are vectors, which can be interpreted as multiple feature maps of size 1x1. Such representations can only convey spatial information implicitly when coupled with powerful decoders. In this work, we propose spatial VAEs that use feature maps of larger size as latent variables to explicitly capture spatial information. This is achieved by allowing the latent variables to be sampled from matrix-variate normal (MVN) distributions whose parameters are computed from the encoder network. To increase dependencies among locations on latent feature maps and reduce the number of parameters, we further propose spatial VAEs via low-rank MVN distributions. Experimental results show that the proposed spatial VAEs outperform original VAEs in capturing rich structural and spatial information.Comment: Accepted by SDM2019. Code is publicly available at https://github.com/divelab/sva

Domain-Indexing Variational Bayes: Interpretable Domain Index for Domain Adaptation

Previous studies have shown that leveraging domain index can significantly boost domain adaptation performance (arXiv:2007.01807, arXiv:2202.03628). However, such domain indices are not always available. To address this challenge, we first provide a formal definition of domain index from the probabilistic perspective, and then propose an adversarial variational Bayesian framework that infers domain indices from multi-domain data, thereby providing additional insight on domain relations and improving domain adaptation performance. Our theoretical analysis shows that our adversarial variational Bayesian framework finds the optimal domain index at equilibrium. Empirical results on both synthetic and real data verify that our model can produce interpretable domain indices which enable us to achieve superior performance compared to state-of-the-art domain adaptation methods. Code is available at https://github.com/Wang-ML-Lab/VDI.Comment: ICLR 2023 Spotlight (notable-top-25%