How can the importance of an input variable in an MLP-based neural network be determined?

To determine the importance of an input variable in an MLP-based neural network, it is essential to consider methods that evaluate the contributions of input features to the model's predictions. The most widely accepted techniques focus on the relationship between input variables and the network's response.

One effective approach is to analyze the weights assigned to each input by the network. These weights reveal how much the neural network relies on an input variable when making decisions. Therefore, calculating the average of the absolute values of parameter estimates or finding the highest absolute value of the parameter estimate would not provide a comprehensive assessment of variable importance, as they don't account for the overall contribution of the input throughout the entire model.

Also, simply multiplying hidden neuron values with input values does not yield a straightforward measure of importance. This method lacks the necessary context to evaluate the significance of input variables across different scenarios.

Overall, the consideration of using none of the above methods points to the understanding that more robust and reliable techniques exist to assess the importance of input variables, such as permutation importance, SHAP values, or analyzing the gradients of the outputs with respect to the inputs. These approaches provide a richer perspective on an input's impact within the model.