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）学习具有挑战性。相比之下，许多已知属性（如空间平滑性或季节性）可以通过在高斯过程（GP）中选择合适的核函数直接建模。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）常用于受强烈季节性影响的遥感领域。我们提出通过组合核函数融合深度学习的优势与GP的清晰建模能力：该组合核将神经网络隐式定义的核与另一个用于建模已知属性（如季节性）的核函数相结合。我们通过结合深度网络与基于Nyström近似的高效映射来实现这一思想，并将其命名为隐式组合核（ICK）。随后采用先采样后优化的方法近似完整GP后验分布。实验表明，ICK在合成数据集和真实数据集上均展现出优越的性能与灵活性。我们相信ICK框架可广泛用于将先验信息融入神经网络的各类应用场景中。