A Review of Heteroscedasticity Treatment with Gaussian Processes and Quantile Regression Meta-models

Antunes, Francisco; O’Sullivan, Aidan; Rodrigues, Filipe; Pereira, Francisco C.

doi:10.1007/978-3-319-40902-3_9

Cited by 8 publications

(9 citation statements)

References 21 publications

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“…. , s 2 nm,m /n m ] T ), where 0.1 is the noise variance of the sensor and 1 T p denotes a row vector of all 1's of length p. The result of this formulation is a heteroscedastic GP, which is an extension to the standard, homoscedastic GP and is often promoted for its improved prediction quality [49]. However, heteroscedasticity is usually treated using additional input-dependent GPs, see e.g.…”

Section: ) Prediction Intervalsmentioning

confidence: 99%

Real-Time Graph Construction Algorithm for Probabilistic Predictions in Vehicular Applications

Ritter

Widmer

Niam

et al. 2021

IEEE Trans. Veh. Technol.

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Reducing the energy consumption of vehicles is one of the greatest challenges we are facing in the mobility sector. A major step in this direction has been taken with the introduction of hybrid electric vehicles. Their performance, however, depends strongly on the energy management strategy used, which exploits the additional degree of freedom of the propulsion system and is inevitably limited by the lack of knowledge about the exact future driving conditions. Various attempts are being made to offer predictions, one of which is to exploit recorded travel data. In this paper, we propose an incremental graph construction algorithm that encapsulates this data in a digital representation of the road network and captures the actual travel routes of the vehicle along with the sequences of the specified measurement signals. The algorithm processes each location estimate separately, together with any desired simultaneously recorded measurement signal such as the vehicle speed, and constructs a directed graph in whose vertices the measurement data is stored. The real-time capability of this algorithm allows an up-to-date representation of both the road network and the signals it contains at all times. Whenever the vehicle is driving on an already visited route, we can obtain distance-resolved predictions by traversing the graph in the direction of travel and querying the stored measurement data. We present two techniques to efficiently store and predict this data, i.e., by using frequentist prediction intervals and Gaussian process regression. Our algorithm runs in real time and without any manual initialization, pre-, or post-processing. Verifications both during real operation on a trolley bus in public transportation and by simulation on a publicly available dataset demonstrate that the algorithm is real-time capable, that it consistently captures and predicts the recorded signals, and that it works in practice.

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Section: ) Prediction Intervalsmentioning

confidence: 99%

Real-Time Graph Construction Algorithm for Probabilistic Predictions in Vehicular Applications

Ritter

Widmer

Niam

et al. 2021

IEEE Trans. Veh. Technol.

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“…For example, applying the functions for the 2.5% and 97.5% quantiles, one trivially determines the 95% prediction interval. The function form of the quantile regression itself can be linear or in splines (Koenker [14]), non-linear, non-parametric with Gaussian processes [15], [16] or vector-valued Reproducing Kernel Hilbert Space (RKHS) [17]. If we apply this principle for a significant number of different quantiles (e.g.…”

Section: Literature Reviewmentioning

confidence: 99%

Beyond Expectation: Deep Joint Mean and Quantile Regression for Spatiotemporal Problems

Rodrigues

Pereira

2020

IEEE Trans. Neural Netw. Learning Syst.

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Spatio-temporal problems are ubiquitous and of vital importance in many research fields. Despite the potential already demonstrated by deep learning methods in modeling spatio-temporal data, typical approaches tend to focus solely on conditional expectations of the output variables being modeled. In this paper, we propose a multi-output multi-quantile deep learning approach for jointly modeling several conditional quantiles together with the conditional expectation as a way to provide a more complete "picture" of the predictive density in spatiotemporal problems.Using two large-scale datasets from the transportation domain, we empirically demonstrate that, by approaching the quantile regression problem from a multi-task learning perspective, it is possible to solve the embarrassing quantile crossings problem, while simultaneously significantly outperforming state-of-the-art quantile regression methods. Moreover, we show that jointly modeling the mean and several conditional quantiles not only provides a rich description about the predictive density that can capture heteroscedastic properties at a neglectable computational overhead, but also leads to improved predictions of the conditional expectation due to the extra information and a regularization effect induced by the added quantiles.

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“…This method has been applied to various problems in, e.g., econometric analysis [19], weather forecasting [20], and transport modeling [9]. The QR model itself can follow either of several functional forms, such as linear or splines [21], non-linear or non-parametric with Gaussian Processes [22,23], or vector-valued [24]. As more quantiles are used, the approximation which QR yields becomes more precise and more robust to artifacts in the true predictive distribution, such as multi-modality and non-symmetry.…”

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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A Review of Heteroscedasticity Treatment with Gaussian Processes and Quantile Regression Meta-models

Cited by 8 publications

References 21 publications

Real-Time Graph Construction Algorithm for Probabilistic Predictions in Vehicular Applications

Real-Time Graph Construction Algorithm for Probabilistic Predictions in Vehicular Applications

Beyond Expectation: Deep Joint Mean and Quantile Regression for Spatiotemporal Problems

Online Predictive Optimization Framework for Stochastic Demand-Responsive Transit Services

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