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

Xiaoming Li, Hubert Normandin-Taillon, Chun Wang, Xiao Huang

TL;DR

This work tackles short-term probabilistic rider demand forecasting in highly volatile Mobility-on-Demand systems by introducing XRMDN, an Extended Recurrent Mixture Density Network. XRMDN leverages three correlated recurrent networks to produce a Gaussian mixture distribution whose parameters are informed by both demand history and exogenous features, enabling accurate uncertainty representation. Empirical results on NY taxi and bike-sharing data show XRMDN achieving superior log-likelihood values, tighter predictive intervals, and competitive point forecasts compared with statistical, ML, and DL baselines, particularly under high volatility. The approach offers a practical tool for better operational planning and decision-making in MoD systems by providing reliable probabilistic forecasts and potential integration with stochastic optimization models.

Abstract

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.

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

TL;DR

This work tackles short-term probabilistic rider demand forecasting in highly volatile Mobility-on-Demand systems by introducing XRMDN, an Extended Recurrent Mixture Density Network. XRMDN leverages three correlated recurrent networks to produce a Gaussian mixture distribution whose parameters are informed by both demand history and exogenous features, enabling accurate uncertainty representation. Empirical results on NY taxi and bike-sharing data show XRMDN achieving superior log-likelihood values, tighter predictive intervals, and competitive point forecasts compared with statistical, ML, and DL baselines, particularly under high volatility. The approach offers a practical tool for better operational planning and decision-making in MoD systems by providing reliable probabilistic forecasts and potential integration with stochastic optimization models.

Abstract

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.
Paper Structure (21 sections, 12 equations, 6 figures, 5 tables, 1 algorithm)

This paper contains 21 sections, 12 equations, 6 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review
  3. The Extended Recurrent Mixture Density Networks for Probabilistic Demand Forecasting
  4. Short-Term Probabilistic Demand Forecasting in MoD
  5. Methodology - XRMDN
  6. Numerical Experiments
  7. Experiment Setup
  8. Data Processing, Feature Selection, and Heteroscedasticity Analysis
  9. New York yellow taxi trip records dataset
  10. UCI Bike-sharing dataset
  11. Evaluation Metrics
  12. Benchmark Models
  13. Statistical Benchmarks
  14. Machine Learning Benchmarks
  15. Deep Learning Benchmarks
  16. ...and 6 more sections

Figures (6)

  • Figure 1: The architecture of XRMDN. WRNN and MRNN are fed with demand sequence data in parallel, the residual is computed by the outputs of WRNN and MRNN, which is applied to concatenate VRNN. For simplicity, we assume there are only two Gaussian components in the architecture.
  • Figure 2: The selected region in Manhattan (NYC yellow taxi trip record dataset)
  • Figure 3: Log-likelihood value comparison of ARIMA, ARIMA-GARCH, RMDN, and XRMDN on the three test sets, (a) DS-1, (b) DS-2, and (C) DS-3
  • Figure 4: Comparison of point forecasting demand results of LSTM, LightGBM, and XRMDN with the observed demand on the three test sets, (a) DS-1, (b) DS-2, and (C) DS-3
  • Figure 5: The sample outcomes from XRMDN under different percentiles on the three test sets, (a) DS-1, (b) DS-2, and (C) DS-3
  • ...and 1 more figures

Theorems & Definitions (1)

  • Definition 1: Time Series Rider Demand Sequence