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Nonlinear Poisson regression using neural networks: a simulation study

Abstract

We describe a novel extension of the Poisson regression model to be based on a multi-layer perceptron, a type of neural network. This relaxes the assumptions of the traditional Poisson regression model, while including it as a special case. In this paper, we describe neural network regression models with six different schemes and compare their performances in three simulated data sets, namely one linear and two nonlinear cases. From the simulation study it is found that the Poisson regression models work well when the linearity assumption is correct, but the neural network models can largely improve the prediction in nonlinear situations.

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Acknowledgments

This study was sponsored by Tehran University of Medical Sciences. Most of this work was carried out during a sabbatical year (student visitor period) of Nader Fallah at the Department of Mathematics and Statistics in Dalhousie University. Authors wish to thank R. Ripley and I. Nabney for their help on R and Matlab Codes. The authors thank Catherine Pretty and Janet Brush for editing this manuscript.

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Correspondence to Kazem Mohammad.

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Fallah, N., Gu, H., Mohammad, K. et al. Nonlinear Poisson regression using neural networks: a simulation study. Neural Comput & Applic 18, 939 (2009). https://doi.org/10.1007/s00521-009-0277-8

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Keywords

  • Generalized linear model
  • Poisson regression
  • Nonlinear regression
  • Multilayer perceptron
  • Simulation