Prediction problems in geographic information science and transportation are often motivated by the possibility to enhance operational efficiency and thereby reduce emissions. Examples range from predicting car sharing demand for relocation planning to forecasting traffic congestion for navigation purposes. However, conventional accuracy metrics ignore the spatial distribution of the errors, despite its relevance for operations. Here, we put forward a spatially aware evaluation metric and loss function based on Optimal Transport (OT). Our framework leverages partial OT and can minimize relocation costs in any spatial prediction problem. We showcase the advantages of OT-based evaluation over conventional metrics and further demonstrate the application of an OT loss function for improving forecasts of bike sharing demand and charging station occupancy.

A new measure of generalisation error called Off Training Set (OTS) er ror was introduced recently in [Wolpert, 1996b, Wolpert, 1996a]. Under quit e weak assumptions it was shown that with respect to OTS error there are no a priori distinctions between learning algorithms, at least if it is assumed that the target functions are uniformly distributed. Thus, as far as OTS error is co ncerned, an algorithm that minimizes error on the training set will do no better tha n random guessing. If OTS error accurately models the concept of generaliz ation then this is a depressing conclusion indeed. However, in this paper it is argued that OTS error does not model wh at is normally meant by generalization error. In particular, it is shown th at the assumptions underlying one of the main "no free lunch" (NFL) theor ems (theorem 2) in [Wolpert, 1996b] imply that the distributions used to genera te training data and testing data have disjoint supports. Thus, training a neu ral network to recognise faces by showing it images of handwrittten character s is the kind of learning problem covered by the NFL theorem.