Heteroscedastic Gaussian processes for uncertainty modeling in large-scale crowdsourced traffic data

Rodrigues, Filipe; Pereira, Francisco C.

doi:10.1016/j.trc.2018.08.007

Cited by 26 publications

(11 citation statements)

References 29 publications

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“…Gaussian processes (GP), which are also known as kernel-based learning algorithms, have become more popular in spatiotemporal research due to their ability to effectively model complex, nonlinear relationships [36]. GP models are very effective tools for investigating implicit correlations between parameters, which makes them particularly effective for complex nonlinear classification and regression analysis [37]. A highly appealing feature of GP models is that they are developed using a Bayesian framework, which enables probabilistic predictions based on the model's parameters.…”

Section: Gaussian Processes (Gp) Modelmentioning

confidence: 99%

“…However, the GP model computational cost is expensive, due to the covariance matrix, where its computational complexity is O(N 3 ) and its memory complexity is O(N 2 ) [41]. This may limit the use of the GP model when N is large, where N is the number of observations [37]. To overcome this issue, a number of studies have suggested reducing the run-time complexity by reducing the number of the parameters, which can be achieved by producing sub-samples of the observations using hierarchical structures [42].…”

Section: Gaussian Processes (Gp) Modelmentioning

confidence: 99%

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Spatiotemporal Traffic Prediction Using Hierarchical Bayesian Modeling

2021

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Hierarchical Bayesian models (HBM) are powerful tools that can be used for spatiotemporal analysis. The hierarchy feature associated with Bayesian modeling enhances the accuracy and precision of spatiotemporal predictions. This paper leverages the hierarchy of the Bayesian approach using the three models; the Gaussian process (GP), autoregressive (AR), and Gaussian predictive processes (GPP) to predict long-term traffic status in urban settings. These models are applied on two different datasets with missing observation. In terms of modeling sparse datasets, the GPP model outperforms the other models. However, the GPP model is not applicable for modeling data with spatial points close to each other. The AR model outperforms the GP models in terms of temporal forecasting. The GP model is used with different covariance matrices: exponential, Gaussian, spherical, and Matérn to capture the spatial correlation. The exponential covariance yields the best precision in spatial analysis with the Gaussian process, while the Gaussian covariance outperforms the others in temporal forecasting.

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Section: Gaussian Processes (Gp) Modelmentioning

confidence: 99%

Section: Gaussian Processes (Gp) Modelmentioning

confidence: 99%

Spatiotemporal Traffic Prediction Using Hierarchical Bayesian Modeling

2021

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“…Prediction of future demand for transport has thus been a long studied research topic, resulting in a plethora of parametric and non-parametric techniques for demand modeling [10,11]. However, despite the importance of accurate demand prediction, previous studies have often tended to over-simplify by providing only point estimates of future values [12]. For example, transport studies often provide only the mean and standard deviation of the predictive distribution, either directly or, respectively, through the center and bounds of a confidence interval.…”

Section: Demand Prediction With Uncertaintymentioning

confidence: 99%

“…In turn, this can lead to inaccurate resource allocation and passenger dissatisfaction. Indeed, there are several benefits for preserving uncertainty in predictions, rather than providing only point estimates [12,17,18]. On one hand, preserving uncertainty conveys a high degree of confidence in the predictions, so that corresponding decisions can be made more intelligently.…”

Section: Demand Prediction With Uncertaintymentioning

confidence: 99%

Online Predictive Optimization Framework for Stochastic Demand-Responsive Transit Services

Peled,

Lee,

Jiang

et al. 2019

Preprint

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This study develops an online predictive optimization framework for dynamically operating a transit service in an area of crowd movements. The proposed framework integrates demand prediction and supply optimization to periodically redesign the service routes based on recently observed demand. To predict demand for the service, we use Quantile Regression to estimate the marginal distribution of movement counts between each pair of serviced locations. The framework then combines these marginals into a joint demand distribution by constructing a Gaussian copula, which captures the structure of correlation between the marginals. For supply optimization, we devise a linear programming model, which simultaneously determines the route structure and the service frequency according to the predicted demand. Importantly, our framework both preserves the uncertainty structure of future demand and leverages this for robust route optimization, while keeping both components decoupled. We evaluate our framework using a real-world case study of autonomous mobility in a university campus in Denmark. The results show that our framework often obtains the ground truth optimal solution, and can outperform conventional methods for route optimization, which do not leverage full predictive distributions.

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“…Further, it reduces model selection efforts to a great extent and facilitates hyper-parameter estimation through the marginal likelihood. These properties have lead to their use in various real world problems [22], active learning [17] and global optimization such as Bayesian optimization [23].…”

Section: Introductionmentioning

confidence: 99%

Improving Robustness and Uncertainty Modelling in Neural Ordinary Differential Equations

Anumasa,

Srijith

2021

Preprint

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Deep learning models such as Resnets have resulted in state-of-the-art accuracy in many computer vision problems. Neural ordinary differential equations (NODE) provides a continuous depth generalization of Resnets and overcome drawbacks of Resnet such as model selection and parameter complexity. Though NODE is more robust than Resnet, we find that NODE based architectures are still far away from providing robustness and uncertainty handling required for many computer vision problems. We propose novel NODE models which address these drawbacks. In particular, we propose Gaussian processes (GPs) to model the fully connected neural networks in NODE (NODE-GP) to improve robustness and uncertainty handling capabilities of NODE. The proposed model is flexible to accommodate different NODE architectures, and further improves the model selection capabilities in NODEs. We also find that numerical techniques play an important role in modelling NODE robustness, and propose to use different numerical techniques to improve NODE robustness. We demonstrate the superior robustness and uncertainty handling capabilities of proposed models on adversarial attacks and out-ofdistribution experiments for the image classification tasks.

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Heteroscedastic Gaussian processes for uncertainty modeling in large-scale crowdsourced traffic data

Cited by 26 publications

References 29 publications

Spatiotemporal Traffic Prediction Using Hierarchical Bayesian Modeling

Spatiotemporal Traffic Prediction Using Hierarchical Bayesian Modeling

Online Predictive Optimization Framework for Stochastic Demand-Responsive Transit Services

Improving Robustness and Uncertainty Modelling in Neural Ordinary Differential Equations

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