This paper proposes a new high dimensional regression method by merging Gaussian process regression into a variational autoencoder framework. In contrast to other regression methods, the proposed method focuses on the case where output responses are on a complex high dimensional manifold, such as images. Our contributions are summarized as follows: (i) A new regression method estimating high dimensional image responses, which is not handled by existing regression algorithms, is proposed. (ii) The proposed regression method introduces a strategy to learn the latent space as well as the encoder and decoder so that the result of the regressed response in the latent space coincide with the corresponding response in the data space. (iii) The proposed regression is embedded into a generative model, and the whole procedure is developed by the variational autoencoder framework. We demonstrate the robustness and effectiveness of our method through a number of experiments on various visual data regression problems.

[Paper][Supplementary] [ppt] [Code (oct, 2017)]

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