Incorporating Prior Knowledge on Features into Learning

In the standard formulation of supervised learning the input is represented as a vector of features. However, in most real-life problems, we also have additional information about each of the features. This information can be represented as a set of properties, referred to as meta-features. For instance, in an image recognition task, where the features are pixels, the meta-features can be the (x, y) position of each pixel. We propose a new learning framework that incorporates meta- features. In this framework we assume that a weight is assigned to each feature, as in linear discrimination, and we use the meta-features to define a prior on the weights. This prior is based on a Gaussian process and the weights are assumed to be a smooth function of the meta-features. Using this framework we derive a practical algorithm that improves gen- eralization by using meta-features and discuss the theoretical advantages of incorporating them into the learning. We apply our framework to design a new kernel for hand-written digit recognition. We obtain higher accuracy with lower computational complexity in the primal representation. Finally, we discuss the applicability of this framework to biological neural networks.