Autoencoders and their variants are among the most widely used models in representation learning and generative modeling. However, autoencoder-based models usually assume that the learned representations are i.i.d. and fail to capture the correlations between the data samples. To address this issue, we propose a novel Sparse Gaussian Process Bayesian Autoencoder (SGPBAE) model in which we impose fully Bayesian sparse Gaussian Process priors on the latent space of a Bayesian Autoencoder. We perform posterior estimation for this model via stochastic gradient Hamiltonian Monte Carlo. We evaluate our approach qualitatively and quantitatively on a wide range of representation learning and generative modeling tasks and show that our approach consistently outperforms multiple alternatives relying on Variational Autoencoders.

翻译：自编码器及其变体是表示学习与生成建模中使用最广泛的模型之一。然而，基于自编码器的模型通常假设学习到的表示是独立同分布的，未能捕捉数据样本间的相关性。为解决这一问题，我们提出了一种新颖的稀疏高斯过程贝叶斯自编码器（SGPBAE）模型，该模型在贝叶斯自编码器的隐空间上施加了全贝叶斯稀疏高斯过程先验。我们通过随机梯度哈密顿蒙特卡洛方法对该模型进行后验估计。我们在广泛的表示学习与生成建模任务上定性和定量地评估了我们的方法，结果表明我们的方法在多个任务上一致优于依赖变分自编码器的多种替代方案。