# XRMDN: An Extended Recurrent Mixture Density Network for Short-Term Probabilistic Rider Demand Forecasting with High Volatility

arXiv: https://arxiv.org/abs/2310.09847 · HTML: https://mlsanity.com/paper/2310.09847/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 47 references that are in the map.
- First posted on arXiv 15 Oct 2023.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [GluonTS: Probabilistic Time Series Models in Python](https://mlsanity.com/paper/1906.05264/) (2019)
- [Predicting Station-level Hourly Demands in a Large-scale Bike-sharing Network: A Graph Convolutional Neural Network Approach](https://mlsanity.com/paper/1712.04997/) (2017)
- [Short-Term Forecasting of Passenger Demand under On-Demand Ride Services: A Spatio-Temporal Deep Learning Approach](https://mlsanity.com/paper/1706.06279/) (2017)
- [Uncertainty Quantification of Sparse Travel Demand Prediction with Spatial-Temporal Graph Neural Networks](https://mlsanity.com/paper/2208.05908/) (2022)
- [Deep-learning Architecture for Short-term Passenger Flow Forecasting in Urban Rail Transit](https://mlsanity.com/paper/1912.12563/) (2019)
- [Cross-Mode Knowledge Adaptation for Bike Sharing Demand Prediction using Domain-Adversarial Graph Neural Networks](https://mlsanity.com/paper/2211.08903/) (2022)

## Built on by (most cited first, 3 of 3)

- [From Samples to Scenarios: A New Paradigm for Probabilistic Forecasting](https://mlsanity.com/paper/2509.19975/) (2025)
- [Autoregressive Boltzmann Generators](https://mlsanity.com/paper/2606.27361/) (2026)
- [Conditional Normalizing Flows for Forward and Backward Joint State and Parameter Estimation](https://mlsanity.com/paper/2601.07013/) (2026)

## Abstract (arXiv)

In the realm of Mobility-on-Demand (MoD) systems, the forecasting of rider demand is a cornerstone for operational decision-making and system optimization. Traditional forecasting methodologies primarily yield point estimates, thereby neglecting the inherent uncertainty within demand projections. Moreover, MoD demand levels are profoundly influenced by both endogenous and exogenous factors, leading to high and dynamic volatility. This volatility significantly undermines the efficacy of conventional time series forecasting methods. In response, we propose an Extended Recurrent Mixture Density Network (XRMDN), a novel deep learning framework engineered to address these challenges. XRMDN leverages a sophisticated architecture to process demand residuals and variance through correlated modules, allowing for the flexible incorporation of endogenous and exogenous data. This architecture, featuring recurrent connections within the weight, mean, and variance neural networks, adeptly captures demand trends, thus significantly enhancing forecasting precision, particularly in high-volatility scenarios. Our comprehensive experimental analysis, utilizing real-world MoD datasets, demonstrates that XRMDN surpasses the existing benchmark models across various metrics, notably excelling in high-demand volatility contexts. This advancement in probabilistic demand forecasting marks a significant contribution to the field, offering a robust tool for enhancing operational efficiency and customer satisfaction in MoD systems.