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Gradient boosting for distributional regression: faster tuning and improved variable selection via noncyclical updates

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Abstract

We present a new algorithm for boosting generalized additive models for location, scale and shape (GAMLSS) that allows to incorporate stability selection, an increasingly popular way to obtain stable sets of covariates while controlling the per-family error rate. The model is fitted repeatedly to subsampled data, and variables with high selection frequencies are extracted. To apply stability selection to boosted GAMLSS, we develop a new “noncyclical” fitting algorithm that incorporates an additional selection step of the best-fitting distribution parameter in each iteration. This new algorithm has the additional advantage that optimizing the tuning parameters of boosting is reduced from a multi-dimensional to a one-dimensional problem with vastly decreased complexity. The performance of the novel algorithm is evaluated in an extensive simulation study. We apply this new algorithm to a study to estimate abundance of common eider in Massachusetts, USA, featuring excess zeros, overdispersion, nonlinearity and spatiotemporal structures. Eider abundance is estimated via boosted GAMLSS, allowing both mean and overdispersion to be regressed on covariates. Stability selection is used to obtain a sparse set of stable predictors.

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Acknowledgements

We thank Mass Audubon for the use of common eider abundance data.

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Authors and Affiliations

  1. Department of Statistics, Ludwig-Maximilians-Universität München, Ludwigstrasse 33, 80539, Munich, Germany

    Janek Thomas & Bernd Bischl

  2. Department of Medical Informatics, Biometry and Epidemiology, FAU Erlangen-Nürnberg, Erlangen, Germany

    Andreas Mayr

  3. Department of Medical Biometry, Informatics and Epidemiology, University Hospital Bonn, Bonn, Germany

    Andreas Mayr & Matthias Schmid

  4. U.S. Fish & Wildlife Service, National Wildlife Refuge System, Southeast Inventory & Monitoring Branch, Lewistown, MT, USA

    Adam Smith

  5. Section Biostatistics, Paul-Ehrlich-Institute, Langen, Germany

    Benjamin Hofner

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  1. Janek Thomas
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  2. Andreas Mayr
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  3. Bernd Bischl
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  4. Matthias Schmid
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  5. Adam Smith
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  6. Benjamin Hofner
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Correspondence to Janek Thomas.

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Thomas, J., Mayr, A., Bischl, B. et al. Gradient boosting for distributional regression: faster tuning and improved variable selection via noncyclical updates. Stat Comput 28, 673–687 (2018). https://doi.org/10.1007/s11222-017-9754-6

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  • DOI: https://doi.org/10.1007/s11222-017-9754-6

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