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.

该论文提出了一种新的高维回归方法，通过将高斯过程回归融合到变分自编码器框架中实现。该方法关注输出响应在复杂高维流形上的情况，例如图像。该方法估计高维图像响应的回归，引入一种学习潜在空间、编码器和解码器的策略，并将回归嵌入到生成模型中，通过变分自编码器框架开发整个过程。作者通过多个实验展示该方法的鲁棒性和有效性。

变分自编码回归: 高维视觉数据在复杂流形上的回归