We revisit the Gaussian process model with spherical harmonic features and study connections between the associated RKHS, its eigenstructure and deep models. Based on this, we introduce a new class of kernels which correspond to deep models of continuous depth. In our formulation, depth can be estimated as a kernel hyper-parameter by optimizing the evidence lower bound. Further, we introduce sparseness in the eigenbasis by variational learning of the spherical harmonic phases. This enables scaling to larger input dimensions than previously, while also allowing for learning of high frequency variations. We validate our approach on machine learning benchmark datasets.

翻译：我们重新探讨了采用球谐特征的高斯过程模型，并研究了关联的再生核希尔伯特空间（RKHS）、其本征结构与深度模型之间的联系。基于此，我们引入了一类与连续深度深度模型相对应的新核函数。在我们的公式中，深度可通过优化证据下界作为核超参数进行估计。此外，我们通过变分学习球谐相位，在本征基中引入稀疏性。这使得我们能够扩展到比以往更大的输入维度，同时还能学习高频变化。我们在机器学习基准数据集上验证了该方法。