Learning from web data is increasingly popular due to abundant free web resources. However, the performance gap between webly supervised learning and traditional supervised learning is still very large, due to the label noise of web data as well as the domain shift between web data and test data. To fill this gap, most existing methods propose to purify or augment web data using instance-level supervision, which generally requires heavy annotation. Instead, we propose to address the label noise

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... and domain shift by using more accessible category-level supervision. In particular, we build our deep probabilistic framework upon variational autoencoder (VAE), in which classification network and VAE can jointly leverage category-level hybrid information. Then, we extend our method for domain adaptation followed by our low-rank refinement strategy. Extensive experiments on three benchmark datasets demonstrate the effectiveness of our proposed method.