A Multi-Horizon Quantile Recurrent Forecaster

Wen, Ruofeng; Torkkola, Kari; Balakrishnan, N.; Madeka, Dhruv

doi:10.48550/arxiv.1711.11053

Cited by 97 publications

(126 citation statements)

References 16 publications

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“…We analyze the generalization errors under multi-horizon and multi-quantile time series forecasting, characterized with quantities, such as the Rademachar complexity and discrepancy measure for stationarity (in Section 6). Under the state-of-theart Seq2Seq MQ-CNN model [29], extensive experiments on real-world datasets demonstrate the consistency and accuracy improvement of our methodology with I(S)QF layers over various other baseline layers, e.g., default quantile [29], Gaussian [7], and SQF [9] (in Section 7).…”

Section: Introductionmentioning

confidence: 79%

“…Fortunately, quantile regression [14,13], which has been successfully used for robustly modeling probabilistic outputs, comes to rescue. The incorporation of the quantile regression component to various sequential neural network backbones has been shown to be particularly effective with recent advances in deep learning [29,9,18,6]. Obtaining a full probabilistic prediction (i.e., the ability to query a forecast at an arbitrary quantile) usually requires generating multiple quantiles at once.…”

Section: Introductionmentioning

confidence: 99%

“…Even though various strategies have been proposed to remedy quantile crossing (See Section 1.1), these techniques are not widely adopted in combination with recent deep probabilistic forecasting models, due to their perceived complexity and lack of solid principles. In particular, Wen et al [29], Lim et al [18] do not explicitly address quantile crossing.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecasting

Park¹,

Maddix²,

Aubet³

et al. 2021

Preprint

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Quantile regression is an effective technique to quantify uncertainty, fit challenging underlying distributions, and often provide full probabilistic predictions through joint learnings over multiple quantile levels. A common drawback of these joint quantile regressions, however, is quantile crossing, which violates the desirable monotone property of the conditional quantile function. In this work, we propose the Incremental (Spline) Quantile Functions I(S)QF, a flexible and efficient distribution-free quantile estimation framework that resolves quantile crossing with a simple neural network layer. Moreover, I(S)QF inter/extrapolate to predict arbitrary quantile levels that differ from the underlying training ones. Equipped with the analytical evaluation of the continuous ranked probability score of I(S)QF representations, we apply our methods to NN-based times series forecasting cases, where the savings of the expensive re-training costs for non-trained quantile levels is particularly significant. We also provide a generalization error analysis of our proposed approaches under the sequence-tosequence setting. Lastly, extensive experiments demonstrate the improvement of consistency and accuracy errors over other baselines.

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Section: Introductionmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecasting

Park¹,

Maddix²,

Aubet³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…State-space models (Durbin & Koopman, 2012;Hyndman et al, 2008a;West et al, 1985) provides a more general and interpretable framework for modeling time series by sequentially updating information to give better estimates; Kalman filter (Welch et al, 1995) and exponential smoothing (Hyndman et al, 2008a) are both prominent examples. Deep Neural Networks (Becker et al, 2019;Krishnan et al, 2015;Lai et al, 2018;Rangapuram et al, 2018;Wen et al, 2017) can improve the ability to model complex data with enough history. However, it is very difficult to obtain single model that works well in diverse situations.…”

Section: Related Workmentioning

confidence: 99%

Dynamic Combination of Heterogeneous Models for Hierarchical Time Series

Han¹,

Hu²,

Ghosh³

2021

Preprint

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We introduce a mixture of heterogeneous experts framework called MECATS, which simultaneously forecasts the values of a set of time series that are related through an aggregation hierarchy. Different types of forecasting models can be employed as individual experts so that the form of each model can be tailored to the nature of the corresponding time series. MECATS learns hierarchical relationships during the training stage to help generalize better across all the time series being modeled and also mitigates coherency issues that arise due to constraints imposed by the hierarchy. We further build multiple quantile estimators on top of the point forecasts. The resulting probabilistic forecasts are nearly coherent, distribution-free, and independent of the choice of forecasting models. We conduct a comprehensive evaluation on both point and probabilistic forecasts and also formulate an extension for situations where change points exist in sequential data. In general, our method is robust, adaptive to datasets with different properties, and highly configurable and efficient for large-scale forecasting pipelines.

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“…However, it's difficult to obtain explicit formulas for modeling the correlation of different dimensions. Methods based on recurrent neural networks [12] or attention [13] usually do not explicitly model the correlation of the data in different dimensions, which limits the prediction performance of the model.…”

Section: Introductionmentioning

confidence: 99%

TFDPM: Attack detection for cyber-physical systems with diffusion probabilistic models

Yan¹,

Zhou²,

Zhan³

et al. 2021

Preprint

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With the development of AIoT, data-driven attack detection methods for cyber-physical systems (CPSs) have attracted lots of attention. However, existing methods usually adopt tractable distributions to approximate data distributions, which are not suitable for complex systems. Besides, the correlation of the data in different channels does not attract sufficient attention. To address these issues, we use energy-based generative models, which are less restrictive on functional forms of the data distribution. In addition, graph neural networks are used to explicitly model the correlation of the data in different channels. In the end, we propose TFDPM, a general framework for attack detection tasks in CPSs. It simultaneously extracts temporal pattern and feature pattern given the historical data. Then extract features are sent to a conditional diffusion probabilistic model. Predicted values can be obtained with the conditional generative network and attacks are detected based on the difference between predicted values and observed values. In addition, to realize real-time detection, a conditional noise scheduling network is proposed to accelerate the prediction process. Experimental results show that TFDPM outperforms existing state-of-the-art attack detection methods. The noise scheduling network increases the detection speed by three times.

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A Multi-Horizon Quantile Recurrent Forecaster

Cited by 97 publications

References 16 publications

Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecasting

Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecasting

Dynamic Combination of Heterogeneous Models for Hierarchical Time Series

TFDPM: Attack detection for cyber-physical systems with diffusion probabilistic models

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