• Corpus ID: 201670525

Deep Learning and MARS: A Connection

@article{Kohler2019DeepLA,
  title={Deep Learning and MARS: A Connection},
  author={Michael Kohler and Adam Krzyżak and Sophie Langer},
  journal={ArXiv},
  year={2019},
  volume={abs/1908.11140}
}
We consider least squares regression estimates using deep neural networks. We show that these estimates satisfy an oracle inequality, which implies that (up to a logarithmic factor) the error of these estimates is at least as small as the optimal possible error bound which one would expect for MARS in case that this procedure would work in the optimal way. As a result we show that our neural networks are able to achieve a dimensionality reduction in case that the regression function locally has… 

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