A maximum entropy approach for the modelling of car-sharing parking dynamics.

The science of cities is a relatively new and interdisciplinary topic aimed at studying and characterizing the collective processes that shape the growth and dynamics of urban populations. Amongst other open problems, the forecast of mobility trends in urban spaces is a lively research topic that aims at assisting the design and implementation of efficient transportation policies and inclusive urban planning. To this end, many Machine-Learning models have been put forward to predict mobility patterns. However, most of them are not interpretable -as they build on complex hidden representations of the system configurations- or do not allow for model inspection, thus limiting our understanding of the underlying mechanisms driving the citizen's daily routines. Here, we tackle this problem by building a fully interpretable statistical model that, incorporating only the minimum number of constraints, can predict different phenomena arising in the city. Using data on the movements of car-sharing vehicles in several Italian cities, we infer a model using the Maximum Entropy (MaxEnt) principle. The model allows for an accurate spatio-temporal prediction of car-sharing vehicles' presence in different city areas and, thanks to its simple yet general formulation, to precisely perform anomaly detection (e.g., detect strikes and bad weather conditions from car-sharing data only). We compare the forecasting capabilities of our model with different state-of-the-art models explicitly made for time-series forecasting: SARIMA models and Deep Learning Models. We find that MaxEnt models are highly predictive, outperforming SARIMAs while having similar performances of deep Neural Networks - but with advantages of being more interpretable, more flexibile-i.e., they can be applied to different tasks- and being computationally efficient. Our results show that statistical inference might play a fundamental role in building robust and general models describing urban systems phenomena.