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）学习过程具有挑战性。相比之下，高斯过程（GP）通过选择适当的核函数，可轻松建模空间平滑性、季节性等已知属性。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，常用于遥感领域的卷积神经网络（CNN）就受到强季节性效应的影响。我们提出利用复合核融合深度学习与GP的明确建模能力，该复合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）的第二核函数。我们通过结合深度网络和基于Nyström近似的高效映射实现这一思想，并将其命名为隐式复合核（ICK）。随后采用"采样-优化"方法近似完整的GP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优越的性能与灵活性。我们相信ICK框架可在众多应用中实现将先验信息融入神经网络。