Modeling Censored Mobility Demand through Quantile Regression Neural Networks

Shared mobility services require accurate demand models for effective service planning. On one hand, modeling the full probability distribution of demand is advantageous, because the full uncertainty structure preserves valuable information for decision making. On the other hand, demand is often observed through usage of the service itself, so that the observations are censored, as they are inherently limited by available supply. Since the 1980s, various works on Censored Quantile Regression models have shown them to perform well under such conditions, and in the last two decades, several works have proposed to implement them flexibly through Neural Networks (CQRNN). However, apparently no works have yet applied CQRNN in the Transport domain. We address this gap by applying CQRNN to datasets from two shared mobility providers in the Copenhagen metropolitan area in Denmark, as well as common synthetic baseline datasets. The results show that CQRNN can estimate the intended distributions better than both censorship-unaware models and parametric censored models.

[1]  Colin Chen.  A Finite Smoothing Algorithm for Quantile Regression , 2007 .

[2]  Chenlei Leng,et al.  A quantile regression estimator for censored data , 2013, 1302.0181.

[3]  Jürgen Schmidhuber,et al.  Long Short-Term Memory , 1997, Neural Computation.

[4]  D. Hensher,et al.  Towards a framework for Mobility-as-a-Service policies , 2020 .

[5]  Jong-Hyeon Jeong,et al.  Deep Learning for Quantile Regression: DeepQuantreg , 2020, ArXiv.

[6]  Naomi S. Altman,et al.  Quantile regression , 2019, Nature Methods.

[7]  Victor O. K. Li,et al.  Deep Multi-Scale Convolutional LSTM Network for Travel Demand and Origin-Destination Predictions , 2020, IEEE Transactions on Intelligent Transportation Systems.

[8]  Jooyong Shim,et al.  Support vector censored quantile regression under random censoring , 2009, Comput. Stat. Data Anal..

[9]  Xuming He,et al.  Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood , 2016 .

[10]  Georgios Giasemidis,et al.  A hybrid model of kernel density estimation and quantile regression for GEFCom2014 probabilistic load forecasting , 2016, 1610.05183.

[11]  T. Mroz,et al.  The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions , 1987 .

[12]  Ali Gannoun,et al.  Non‐parametric Quantile Regression with Censored Data , 2005 .

[13]  J. Powell,et al.  Least absolute deviations estimation for the censored regression model , 1984 .

[14]  Haiyan Li,et al.  Probability density forecasting of wind power using quantile regression neural network and kernel density estimation , 2018 .

[15]  G. Carlier,et al.  Vector Quantile Regression , 2014, 1406.4643.

[16]  Alexander Hanbo Li,et al.  Censored Quantile Regression Forest , 2020, AISTATS.

[17]  Moshe Buchinsky.  Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research , 1998 .

[18]  Fan Yang,et al.  Probabilistic Airport Traffic Demand Prediction Incorporating the Weather Factors , 2020 .

[19]  Chao Wang,et al.  Electricity consumption probability density forecasting method based on LASSO-Quantile Regression Neural Network , 2019, Applied Energy.

[20]  R. Koenker,et al.  Regression Quantiles , 2007 .

[21]  James W. Taylor.  A Quantile Regression Neural Network Approach to Estimating the Conditional Density of Multiperiod Returns , 2000 .

[22]  Alex J. Cannon.  Quantile regression neural networks: Implementation in R and application to precipitation downscaling , 2011, Comput. Geosci..

[23]  Francisco C. Pereira,et al.  Estimating Latent Demand of Shared Mobility through Censored Gaussian Processes , 2020, Transportation Research Part C: Emerging Technologies.

[24]  Dipti Srinivasan,et al.  An Improved Quantile Regression Neural Network for Probabilistic Load Forecasting , 2019, IEEE Transactions on Smart Grid.

[25]  Peter Nijkamp,et al.  Neural Networks in Transport Applications , 1998 .

[26]  Songfeng Zheng,et al.  QBoost: Predicting quantiles with boosting for regression and binary classification , 2012, Expert Syst. Appl..

[27]  Julian Stander,et al.  Bayesian analysis of a Tobit quantile regression model , 2007 .

[28]  Carlos Lamarche,et al.  Estimation of Censored Quantile Regression for Panel Data With Fixed Effects , 2013 .

[29]  Jung-Yu Cheng,et al.  Quantile regression of right-censored length-biased data using the Buckley–James-type method , 2014, Comput. Stat..

[30]  Amanda E. Kowalski,et al.  Quantile Regression with Censoring and Endogeneity , 2011 .

[31]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[32]  Wanying Zhang,et al.  Probability density forecasting of wind power based on multi-core parallel quantile regression neural network , 2020, Knowl. Based Syst..

[33]  J. Tobin.  Estimation of Relationships for Limited Dependent Variables , 1958 .

[34]  Stephen Portnoy,et al.  Censored Regression Quantiles , 2003 .

[35]  Justin Dauwels,et al.  Preserving Uncertainty in Demand Prediction for Autonomous Mobility Services , 2019, 2019 IEEE Intelligent Transportation Systems Conference (ITSC).

[36]  G. Santos.  Sustainability and Shared Mobility Models , 2018, Sustainability.

[37]  Gilbert Laporte,et al.  Shared mobility systems: an updated survey , 2018, Ann. Oper. Res..

[38]  Carl E. Rasmussen,et al.  Evaluating Predictive Uncertainty Challenge , 2005, MLCW.

[39]  Francisco C. Pereira,et al.  Beyond Expectation: Deep Joint Mean and Quantile Regression for Spatiotemporal Problems. , 2018, IEEE transactions on neural networks and learning systems.

[40]  Nitish Srivastava,et al.  Dropout: a simple way to prevent neural networks from overfitting , 2014, J. Mach. Learn. Res..

[41]  R. Koenker,et al.  An interior point algorithm for nonlinear quantile regression , 1996 .