In this paper, we introduce a non-crossing quantile (NQ) network for conditional distribution learning. By leveraging non-negative activation functions, the NQ network ensures that the learned distributions remain monotonic, effectively addressing the issue of quantile crossing. Furthermore, the NQ network-based deep distributional learning framework is highly adaptable, applicable to a wide range of applications, from classical non-parametric quantile regression to more advanced tasks such as causal effect estimation and distributional reinforcement learning (RL). We also develop a comprehensive theoretical foundation for the deep NQ estimator and its application to distributional RL, providing an in-depth analysis that demonstrates its effectiveness across these domains. Our experimental results further highlight the robustness and versatility of the NQ network.

Accurate spatial-temporal prediction of network-based travelers' requests is crucial for the effective policy design of ridesharing platforms. Having knowledge of the total demand between various locations in the upcoming time slots enables platforms to proactively prepare adequate supplies, thereby increasing the likelihood of fulfilling travelers' requests and redistributing idle drivers to areas with high potential demand to optimize the global supply-demand equilibrium. This paper delves into the prediction of Origin-Destination (OD) demands at a fine-grained spatial level, especially when confronted with an expansive set of local regions. While this task holds immense practical value, it remains relatively unexplored within the research community. To fill this gap, we introduce a novel prediction model called OD-CED, which comprises an unsupervised space coarsening technique to alleviate data sparsity and an encoder-decoder architecture to capture both semantic and geographic dependencies. Through practical experimentation, OD-CED has demonstrated remarkable results. It achieved an impressive reduction of up to 45% reduction in root-mean-square error and 60% in weighted mean absolute percentage error over traditional statistical methods when dealing with OD matrices exhibiting a sparsity exceeding 90%.