Learning the true density in high-dimensional feature spaces is a well-known problem in machine learning. In this work, we improve the recent Wasserstein autoencoders (WAEs) by proposing Coulomb autoencoders. We demonstrate that a source of sub-optimality in WAEs is the choice of kernel function, because of the additional local minima in the objective. To mitigate this problem, we propose to use Coulomb kernels. We show that, under some conditions on the capacity of the encoder and the decoder, global convergence in the function space can be achieved. Finally, we provide an upper bound on the generalization performance, which can be improved by increasing the capacity of the encoder and the decoder networks. The theory is corroborated by experimental comparisons on synthetic and real-world datasets against several approaches from the families of generative adversarial networks and autoencoder-based models.
翻译:在机器学习中,学习高维特征空间的真正密度是一个众所周知的问题。 在这项工作中,我们通过提出库伦普自动编码器改进了最近的瓦塞斯坦自动编码器(WAEs),我们证明,由于目标中增加了局部微型,WAE中一个亚优化来源是内核功能的选择。为了缓解这一问题,我们提议使用库伦内核。我们表明,在编码器和解密器能力的某些条件下,功能空间的全球趋同是可以实现的。最后,我们提供了通用性能的上限,可以通过提高编码器和解密器网络的能力加以改进。关于合成和真实世界数据集的实验性比较与基因对抗网络和自动编码器模型组合的若干方法的实验性比较证实了这一理论。