Learning travel time distributions with deep generative model

Travel time estimation of a given route with respect to real-time traffic condition is extremely useful for many applications like route planning. We argue that it is even more useful to estimate the travel time distribution, from which we can derive the expected travel time as well as the uncertainty. In this paper, we develop a deep generative model - DeepGTT - to learn the travel time distribution for any route by conditioning on the real-time traffic. DeepGTT interprets the generation of travel time using a three-layer hierarchical probabilistic model. In the first layer, we present two techniques, amortization and spatial smoothness embeddings, to share statistical strength among different road segments; a convolutional neural net based representation learning component is also proposed to capture the dynamically changing real-time traffic condition. In the middle layer, a nonlinear factorization model is developed to generate auxiliary random variable i.e., speed. The introduction of this middle layer separates the statical spatial features from the dynamically changing real-time traffic conditions, allowing us to incorporate the heterogeneous influencing factors into a single model. In the last layer, an attention mechanism based function is proposed to collectively generate the observed travel time. DeepGTT describes the generation process in a reasonable manner, and thus it not only produces more accurate results but also is more efficient. On a real-world large-scale data set, we show that DeepGTT produces substantially better results than state-of-the-art alternatives in two tasks: travel time estimation and route recovery from sparse trajectory data.