Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition
Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition
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发表时间：
2021-06
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通讯作者：
Shengyang Sun-;Jiaxin Shi;A. Wilson;R. Grosse
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作者：
Shengyang Sun-;Jiaxin Shi;A. Wilson;R. Grosse
我们引入了一个新的可扩展的变分高斯过程近似，它提供了一个高保真度的近似，同时保持普遍适用性。我们提出了谐波核分解（HKD），它使用傅立叶级数分解的核作为正交核的总和。我们的变分近似利用这种正交性，使大量的诱导点在一个低的计算成本。我们证明，在一系列的回归和分类问题，我们的方法可以利用输入空间的对称性，如翻译和反射，它显着优于标准的变分方法的可扩展性和准确性。值得注意的是，我们的方法在纯GP模型中的CIFAR-10上实现了最先进的结果。
We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We propose the harmonic kernel decomposition (HKD), which uses Fourier series to decompose a kernel as a sum of orthogonal kernels. Our variational approximation exploits this orthogonality to enable a large number of inducing points at a low computational cost. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections, and it significantly outperforms standard variational methods in scalability and accuracy. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.