Pseudo-Solution of Weight Equations in Neural Networks: Application for Statistical Parameters Estimation

  • Vincent J. M. Kiki
  • Villévo Adanhounme
  • Mahouton Norbert Hounkonnou
Part of the STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health book series (STEAM)


An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is implemented for the approximation of smooth batch data containing input–output of the hidden neurons and the final neural output of the network. The training set is associated with the adjustable parameters of the network by weight equations that may be compatible or incompatible.Then we have obtained the exact input weight of the nonlinear equations and the approximated output weight of the linear equations using the conjugate gradient method with an adaptive learning rate. Using the multi-agent system as the different rates of traders of five regions in the Republic of Benin smuggling the fuel from the Federal Republic of Nigeria and the computational neural networks, one can predict the average rates of fuel smuggling traders thinking of this activity in terms of its dangerous character and those susceptible to give up this activity, respectively. This information enables the planner or the decision-maker to compare alternative actions, to select the best one for ensuring the retraining of these traders.


Function approximation Conjugate gradient method Adaptive training 



This work is partially supported by the ICTP through the OEA-ICMPA-Prj-15. The ICMPA is in partnership with the Daniel Iagolnitzer Foundation (DIF), France. The authors would like to thank the Konida National Foundation for Scientific Researches (KNFSR) for its financial support.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Vincent J. M. Kiki
    • 1
  • Villévo Adanhounme
    • 2
  • Mahouton Norbert Hounkonnou
    • 2
  1. 1.Ecole Nationale d’Economie Appliquée et de ManagementUniversité d’Abomey-CalaviCotonouBenin
  2. 2.University of Abomey-Calavi, International Chair in Mathematical Physics and Applications(ICMPA)CotonouBenin

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