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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 Gaussianprocess (GP). Many deep learning applications could be enhanced by modelingsuch known properties. For example, convolutional neural networks (CNNs) arefrequently used in remote sensing, which is subject to strong seasonal effects.We propose to blend the strengths of deep learning and the clear modelingcapabilities of GPs by using a composite kernel that combines a kernelimplicitly defined by a neural network with a second kernel function chosen tomodel known properties (e.g., seasonality). We implement this idea by combininga deep network and an efficient mapping based on the Nystrom approximation,which we call Implicit Composite Kernel (ICK). We then adopt asample-then-optimize approach to approximate the full GP posteriordistribution. We demonstrate that ICK has superior performance and flexibilityon both synthetic and real-world data sets. We believe that ICK framework canbe used to include prior information into neural networks in many applications.

Incorporating Prior Knowledge into Neural Networks through an Implicit Composite Kernel