Researching sensitivity of neural network models using analysis of finite fluctuations

Abstract

Building a mathematical model of a complicated system often involves evaluating the influence of the studied inputs (arguments, factors) on the response, identifying important relationships between the used variables, and reducing the model by reducing the number of its inputs. These problems refer to factor sensitivity analysis of mathematical models, the variety of existing methods of which can be divided into five large groups, depending on the used approach and the interpretation of the obtained results. Previously, the authors proposed an alternative approach based on analysis of finite fluctuations using a finite Lagrange increment model to estimate the contribution of finite changes of function variables to finite changes of its value. This article investigates the presented approach by the example of a class of fully connected neural network models. As a result of the above sensitivity analysis, we obtain a set of coefficients estimates determing the sensitivity of each input. For their averaging, we propose to use a point and interval estimation algorithm that uses a weighted Tukey’s average. A comparison of the described method of sensitivity analysis with the well-known Garson’s algorithm and Sobol’ coefficient computation is presented; consistency of the proposed method is shown. The computational stability of the procedure for finding estimates of the influence of inputs is investigated. As a numerical example, we consider a system consisting of two neural network models united by common inputs and having correlated outputs. It is shown that in this case, the sensitivity of the model can be compared in measure and direction with the correlation of outputs and corresponding inputs of the system. Numerical experiments were performed on the neuraldat data set of the NeuralNetTools library of the data processing language R.