Multivariate Quantile Function Forecaster

Kelvin Kan, François-Xavier Aubet, Tim Januschowski, Youngsuk Park, Konstantinos Benidis, Lars Ruthotto, Jan Gasthaus
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:10603-10621, 2022.

Abstract

We propose Multivariate Quantile Function Forecaster (MQF2), a global probabilistic forecasting method constructed using a multivariate quantile function and investigate its application to multi-horizon forecasting. Prior approaches are either autoregressive, implicitly capturing the dependency structure across time but exhibiting error accumulation with increasing forecast horizons, or multi-horizon sequence-to-sequence models, which do not exhibit error accumulation, but also do typically not model the dependency structure across time steps. MQF2 combines the benefits of both approaches, by directly making predictions in the form of a multivariate quantile function, defined as the gradient of a convex function which we parametrize using input-convex neural networks. By design, the quantile function is monotone with respect to the input quantile levels and hence avoids quantile crossing. We provide two options to train MQF2: with energy score or with maximum likelihood. Experimental results on real-world and synthetic datasets show that our model has comparable performance with state-of-the-art methods in terms of single time step metrics while capturing the time dependency structure.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-kan22a, title = { Multivariate Quantile Function Forecaster }, author = {Kan, Kelvin and Aubet, Fran\c{c}ois-Xavier and Januschowski, Tim and Park, Youngsuk and Benidis, Konstantinos and Ruthotto, Lars and Gasthaus, Jan}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {10603--10621}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/kan22a/kan22a.pdf}, url = {https://proceedings.mlr.press/v151/kan22a.html}, abstract = { We propose Multivariate Quantile Function Forecaster (MQF2), a global probabilistic forecasting method constructed using a multivariate quantile function and investigate its application to multi-horizon forecasting. Prior approaches are either autoregressive, implicitly capturing the dependency structure across time but exhibiting error accumulation with increasing forecast horizons, or multi-horizon sequence-to-sequence models, which do not exhibit error accumulation, but also do typically not model the dependency structure across time steps. MQF2 combines the benefits of both approaches, by directly making predictions in the form of a multivariate quantile function, defined as the gradient of a convex function which we parametrize using input-convex neural networks. By design, the quantile function is monotone with respect to the input quantile levels and hence avoids quantile crossing. We provide two options to train MQF2: with energy score or with maximum likelihood. Experimental results on real-world and synthetic datasets show that our model has comparable performance with state-of-the-art methods in terms of single time step metrics while capturing the time dependency structure. } }
Endnote
%0 Conference Paper %T Multivariate Quantile Function Forecaster %A Kelvin Kan %A François-Xavier Aubet %A Tim Januschowski %A Youngsuk Park %A Konstantinos Benidis %A Lars Ruthotto %A Jan Gasthaus %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-kan22a %I PMLR %P 10603--10621 %U https://proceedings.mlr.press/v151/kan22a.html %V 151 %X We propose Multivariate Quantile Function Forecaster (MQF2), a global probabilistic forecasting method constructed using a multivariate quantile function and investigate its application to multi-horizon forecasting. Prior approaches are either autoregressive, implicitly capturing the dependency structure across time but exhibiting error accumulation with increasing forecast horizons, or multi-horizon sequence-to-sequence models, which do not exhibit error accumulation, but also do typically not model the dependency structure across time steps. MQF2 combines the benefits of both approaches, by directly making predictions in the form of a multivariate quantile function, defined as the gradient of a convex function which we parametrize using input-convex neural networks. By design, the quantile function is monotone with respect to the input quantile levels and hence avoids quantile crossing. We provide two options to train MQF2: with energy score or with maximum likelihood. Experimental results on real-world and synthetic datasets show that our model has comparable performance with state-of-the-art methods in terms of single time step metrics while capturing the time dependency structure.
APA
Kan, K., Aubet, F., Januschowski, T., Park, Y., Benidis, K., Ruthotto, L. & Gasthaus, J.. (2022). Multivariate Quantile Function Forecaster . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:10603-10621 Available from https://proceedings.mlr.press/v151/kan22a.html.

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