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This paper proposes a new high dimensional regression method by mergingGaussian process regression into a variational autoencoder framework. Incontrast to other regression methods, the proposed method focuses on the casewhere output responses are on a complex high dimensional manifold, such asimages. Our contributions are summarized as follows: (i) A new regressionmethod estimating high dimensional image responses, which is not handled byexisting regression algorithms, is proposed. (ii) The proposed regressionmethod introduces a strategy to learn the latent space as well as the encoderand decoder so that the result of the regressed response in the latent spacecoincide with the corresponding response in the data space. (iii) The proposedregression is embedded into a generative model, and the whole procedure isdeveloped by the variational autoencoder framework. We demonstrate therobustness and effectiveness of our method through a number of experiments onvarious visual data regression problems.

Variational Autoencoded Regression: High Dimensional Regression of Visual Data on Complex Manifold