Learning landscapes: regression on discrete spaces

It is often useful to be able to reconstruct landscapes from a set of data points sampled from the landscape. Neural networks and other supervised learning techniques can accomplish this task but typically do not exploit the metric structure of discrete input spaces. We propose a new method based on Gaussian processes which reconstructs landscapes over discrete spaces from data sampled from the landscape and optional prior beliefs about the correlation structure of the landscape. In addition to speeding up costly fitness evaluations, the methods can be used to characterize landscapes in terms of a small set of easily interpretable quantities