Deep Probabilistic Forecasting of Multivariate Count Data With “Sums and Shares” Distributions: A Case Study on Pedestrian Counts in a Multimodal Transport Hub

Abstract

Forecasting counts data in transportation areas can enrich passenger information for public transport passengers, who may thus better plan their trips. Moreover, forecasting with uncertainty is particularly important in the transportation domain, where the risk of poorly managed high demand is to be avoided. In this paper, we propose a new probabilistic prediction model well-suited for multivariate, overdispersed, and possibly correlated count data. This model combines the strength of the deep learning framework with the modeling of counts data allowed by “sums and shares” distributions. Indeed, deep learning models can handle uncertainty by relying on an abstraction of contextual data and by assuming output distributions. Our model learns a latent representation of the input data with the help of a recurrent neural network and then translates it into multivariate count predictions with a “sums and shares” distribution, well suited to tackle multivariate overdispersed and correlated count data. An extensive benchmark of the proposed model is carried out. We compare this model with seven others from the state-of-the-art probabilistic forecasting models using five open-source data (bikes, taxis, railways, traffic, wikipedia) and a specific use case on pedestrian counts within a multimodal transport hub in the Paris Region. Our model outperforms other models in situations where the data present temporal regularities. The results also highlight the potential of our model in the specific use case. Moreover, this forecasting represents an interesting way to predict short-term pedestrian counts in response to different events, such as concerts or transport disruptions.