Extracting the contribution of independent variables in neural network models: a new approach to handle instability

Abstract

One of the main limitations of Artificial Neural Networks (ANN) is their high inability to know in an explicit way the relations established between explanatory variables (input) and dependent variables (output). This is a major reason why they are usually called "black boxes". In the last few years several methods have been proposed to assess the relative importance of each explanatory variable. Nevertheless, it has not been possible to reach a consensus on which is the best-performing method. This is largely due to the different relative importance obtained for each variable depending on the method used. This importance also varies with the designed network architecture and/or with the initial random weights used to train the ANN. This paper proposes a procedure that seeks to minimize these problems and provides consistency in the results obtained from different methods. Essentially, the idea is to work with a set of neural networks instead of a single one. The proposed procedure is validated using a database collected from a customer satisfaction survey which was conducted on the public transport system of Granada (Spain) in 2007. The results show that, when each method is applied independently, the variable's importance rankings are similar and, in addition, coincide with the hierarchy established by researchers who have applied other techniques.

The identification of relationships between selected honey parameters by extracting the contribution of independent variables in a neural network model

“…According to the reports published by other authors, the results' similarity is not the rule. Even if the results obtained using the selected methods are comparable, the percentage influence of input variables on output variables is different for each method [25,26,52]. The phenomenon described above can be observed also in the results presented in this work.…”

“…Nourani et al [25] used four different methods to investigate the effect of each input parameter on the output in an ANN model of the evaporation process at different climatologic regimes. The compare analysis of variable contribution determination methods has been carried out by de Ona and Garrido [26] based on the model of the Granada Area Transport Consortium customer service quality. Paliwal and Kumar [27] have proposed the new approach to interpreting the relative importance of independent variables in neural networks based on connection weights values and have compared it with the other connection weights method.…”

Preliminary Modeling of an Industrial Recombinant Human Erythropoietin Purification Process by Artificial Neural Networks

“…This is a major reason why they are usually called "black boxes" (De Oña and Garrido, 2014). This arises from the fact that the internal characteristic of a trained network is a set of numbers that are very difficult to relate back to the application in a meaningful fashion (Paliwal and Kumar, 2011).…”

“…This arises from the fact that the internal characteristic of a trained network is a set of numbers that are very difficult to relate back to the application in a meaningful fashion (Paliwal and Kumar, 2011). In the last few years, several methods have been proposed to assess the relative importance of each explanatory variable (Olden and Jackson, 2002;Olden et al, 2004;Papadokonstantakis et al, 2006;Watts and Worner, 2008;Paliwal and Kumar, 2011;Cortez and Embrechts, 2013;De Oña and Garrido, 2014). Nevertheless, it has not been possible to reach a consensus on which is the best-performing method.…”

“…Nevertheless, it has not been possible to reach a consensus on which is the best-performing method. Despite the variety of methods studied, there is no general consensus on which model is the best for determining the contribution of variables (De Oña and Garrido, 2014).…”