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

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.