Probabilistic Forecasting with Spline Quantile Function RNNs

Jan Gasthaus, Konstantinos Benidis, Yuyang Wang, Syama Sundar Rangapuram, David Salinas, Valentin Flunkert, Tim Januschowski
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:1901-1910, 2019.

Abstract

In this paper, we propose a flexible method for probabilistic modeling with conditional quantile functions using monotonic regression splines. The shape of the spline is parameterized by a neural network whose parameters are learned by minimizing the continuous ranked probability score. Within this framework, we propose a method for probabilistic time series forecasting, which combines the modeling capacity of recurrent neural networks with the flexibility of a spline-based representation of the output distribution. Unlike methods based on parametric probability density functions and maximum likelihood estimation, the proposed method can flexibly adapt to different output distributions without manual intervention. We empirically demonstrate the effectiveness of the approach on synthetic and real-world data sets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-gasthaus19a, title = {Probabilistic Forecasting with Spline Quantile Function RNNs}, author = {Gasthaus, Jan and Benidis, Konstantinos and Wang, Yuyang and Rangapuram, Syama Sundar and Salinas, David and Flunkert, Valentin and Januschowski, Tim}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {1901--1910}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/gasthaus19a/gasthaus19a.pdf}, url = {https://proceedings.mlr.press/v89/gasthaus19a.html}, abstract = {In this paper, we propose a flexible method for probabilistic modeling with conditional quantile functions using monotonic regression splines. The shape of the spline is parameterized by a neural network whose parameters are learned by minimizing the continuous ranked probability score. Within this framework, we propose a method for probabilistic time series forecasting, which combines the modeling capacity of recurrent neural networks with the flexibility of a spline-based representation of the output distribution. Unlike methods based on parametric probability density functions and maximum likelihood estimation, the proposed method can flexibly adapt to different output distributions without manual intervention. We empirically demonstrate the effectiveness of the approach on synthetic and real-world data sets.} }
Endnote
%0 Conference Paper %T Probabilistic Forecasting with Spline Quantile Function RNNs %A Jan Gasthaus %A Konstantinos Benidis %A Yuyang Wang %A Syama Sundar Rangapuram %A David Salinas %A Valentin Flunkert %A Tim Januschowski %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-gasthaus19a %I PMLR %P 1901--1910 %U https://proceedings.mlr.press/v89/gasthaus19a.html %V 89 %X In this paper, we propose a flexible method for probabilistic modeling with conditional quantile functions using monotonic regression splines. The shape of the spline is parameterized by a neural network whose parameters are learned by minimizing the continuous ranked probability score. Within this framework, we propose a method for probabilistic time series forecasting, which combines the modeling capacity of recurrent neural networks with the flexibility of a spline-based representation of the output distribution. Unlike methods based on parametric probability density functions and maximum likelihood estimation, the proposed method can flexibly adapt to different output distributions without manual intervention. We empirically demonstrate the effectiveness of the approach on synthetic and real-world data sets.
APA
Gasthaus, J., Benidis, K., Wang, Y., Rangapuram, S.S., Salinas, D., Flunkert, V. & Januschowski, T.. (2019). Probabilistic Forecasting with Spline Quantile Function RNNs. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:1901-1910 Available from https://proceedings.mlr.press/v89/gasthaus19a.html.

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