  Origin-Destination (O-D) travel demand prediction is a fundamental challenge
in transportation. Recently, spatial-temporal deep learning models demonstrate
the tremendous potential to enhance prediction accuracy. However, few studies
tackled the uncertainty and sparsity issues in fine-grained O-D matrices. This
presents a serious problem, because a vast number of zeros deviate from the
Gaussian assumption underlying the deterministic deep learning models. To
address this issue, we design a Spatial-Temporal Zero-Inflated Negative
Binomial Graph Neural Network (STZINB-GNN) to quantify the uncertainty of the
sparse travel demand. It analyzes spatial and temporal correlations using
diffusion and temporal convolution networks, which are then fused to
parameterize the probabilistic distributions of travel demand. The STZINB-GNN
is examined using two real-world datasets with various spatial and temporal
resolutions. The results demonstrate the superiority of STZINB-GNN over
benchmark models, especially under high spatial-temporal resolutions, because
of its high accuracy, tight confidence intervals, and interpretable parameters.
The sparsity parameter of the STZINB-GNN has physical interpretation for
various transportation applications.
