It is challenging to guide neural network (NN) learning with prior knowledge. In contrast, many known properties, such as spatial smoothness or seasonality, are straightforward to model by choosing an appropriate kernel in a Gaussian process (GP). Many deep learning applications could be enhanced by modeling such known properties. For example, convolutional neural networks (CNNs) are frequently used in remote sensing, which is subject to strong seasonal effects. We propose to blend the strengths of deep learning and the clear modeling capabilities of GPs by using a composite kernel that combines a kernel implicitly defined by a neural network with a second kernel function chosen to model known properties (e.g., seasonality). We implement this idea by combining a deep network and an efficient mapping based on the Nystrom approximation, which we call Implicit Composite Kernel (ICK). We then adopt a sample-then-optimize approach to approximate the full GP posterior distribution. We demonstrate that ICK has superior performance and flexibility on both synthetic and real-world data sets. We believe that ICK framework can be used to include prior information into neural networks in many applications.

翻译：将先验知识融入神经网络（NN）学习过程颇具挑战性。相比之下，在高斯过程（GP）中通过选择合适的核函数即可直接建模许多已知属性，例如空间平滑性或季节性。许多深度学习应用可通过建模此类已知属性得到增强。例如，卷积神经网络（CNN）常用于受强季节性效应影响的遥感领域。我们提出通过复合核融合深度学习与高斯过程的清晰建模能力：该核结合了神经网络隐式定义的核函数与用于建模已知属性（如季节性）的第二个核函数。我们通过将深度网络与基于奈斯特罗姆近似的有效映射相结合来实现这一思想，并将其称为隐式复合核（ICK）。随后采用"先采样后优化"方法近似完整的高斯过程后验分布。实验表明，ICK在合成数据集和真实世界数据集上均展现出卓越的性能与灵活性。我们相信ICK框架可广泛应用于将先验信息融入神经网络的各类场景。