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.
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本文重新审视具有球面谐波特征的高斯过程模型,并研究相关的RKHS、特征值结构以及深度模型之间的联系。基于此,本文提出了一类新的核函数,对应于连续深度的深度模型。在我们的计算框架中,深度可以通过优化证据下界来估计为核超参数。此外,我们使用变分学习球面谐波相位引入特征基的稀疏性。这使得我们的方法能够处理比以前更大的输入维度,同时也可以学习高频变化。我们在机器学习基准数据集上验证了我们的方法。