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的学习过程颇具挑战。相比之下，高斯过程（GP）中通过选择合适核函数即可直接建模诸多已知性质（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性质得到增强。例如，在受强季节性效应影响的遥感领域，卷积神经网络（CNN）被广泛使用。我们提出通过复合核融合深度学习优势与GP的清晰建模能力——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性质（如季节性）的第二核函数。具体实现中，我们采用基于Nyström近似的深度网络与高效映射组合方案，称之为隐式复合核（ICK）。进而采用"先采样后优化"方法近似完整的GP后验分布。实验表明，ICK在合成数据集与真实数据集上均展现出卓越的性能与灵活性。我们认为ICK框架可广泛应用于将先验信息融入各类神经网络场景。