Human mobility is well described by closed-form gravity-like models learned automatically from data

Modeling of human mobility is critical to address questions in urban planning and transportation, as well as global challenges in sustainability, public health, and economic development. However, our understanding and ability to model mobility flows within and between urban areas are still incomplete. At one end of the modeling spectrum we have simple so-called gravity models, which are easy to interpret and provide modestly accurate predictions of mobility flows. At the other end, we have complex machine learning and deep learning models, with tens of features and thousands of parameters, which predict mobility more accurately than gravity models at the cost of not being interpretable and not providing insight on human behavior. Here, we show that simple machine-learned, closed-form models of mobility are able to predict mobility flows more accurately, overall, than either gravity or complex machine and deep learning models. At the same time, these models are simple and gravity-like, and can be interpreted in terms similar to standard gravity models. Furthermore, these models work for different datasets and at different scales, suggesting that they may capture the fundamental universal features of human mobility.

Consistencies and inconsistencies between model selection and link prediction in networks

A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand, discounting statistical fluctuations. This problem can be approached using two principled criteria that at first may seem equivalent: selecting the most plausible model in terms of its posterior probability; or selecting the model with the highest predictive performance in terms of identifying missing links. Here we show that while these two approaches yield consistent results in most of cases, there are also notable instances where they do not, that is, where the most plausible model is not the most predictive. We show that in the latter case the improvement of predictive performance can in fact lead to overfitting both in artificial and empirical settings. Furthermore, we show that, in general, the predictive performance is higher when we average over collections of models that are individually less plausible, than when we consider only the single most plausible model.