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Fusing sufficient dimension reduction with neural networks

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  • Kapla, Daniel
  • Fertl, Lukas
  • Bura, Efstathia

Abstract

Neural networks are combined with sufficient dimension reduction methodology in order to remove the limitation of small p and n of the latter. NN-SDR applies when the dependence of the response Y on a set of predictors X is fully captured by the regression function g(B′X), for an unknown function g and low rank parameter B matrix. It is shown that the proposed estimator is on par with competing sufficient dimension reduction methods, such as minimum average variance estimation and conditional variance estimation, in small p and n settings in simulations. Its main advantage is its scalability in regressions with large data, for which the other methods are infeasible.

Suggested Citation

  • Kapla, Daniel & Fertl, Lukas & Bura, Efstathia, 2022. "Fusing sufficient dimension reduction with neural networks," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:csdana:v:168:y:2022:i:c:s0167947321002243
    DOI: 10.1016/j.csda.2021.107390
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    References listed on IDEAS

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    1. Efstathia Bura & Sabrina Duarte & Liliana Forzani, 2016. "Sufficient Reductions in Regressions With Exponential Family Inverse Predictors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1313-1329, July.
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    Cited by:

    1. Zhang, Xin & Zhao, Junlong, 2024. "Group variable selection via group sparse neural network," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).

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