A Quantified Sensitivity Measure for Multilayer Perceptron to Input Perturbation

Abstract

The sensitivity of a neural network's output to its input perturbation is an important issue with both theoretical and practical values. In this article, we propose an approach to quantify the sensitivity of the most popular and general feedforward network: multilayer perceptron (MLP). The sensitivity measure is defined as the mathematical expectation of output deviation due to expected input deviation with respect to overall input patterns in a continuous interval. Based on the structural characteristics of the MLP, a bottom-up approach is adopted. A single neuron is considered first, and algorithms with approximately derived analytical expressions that are functions of expected input deviation are given for the computation of its sensitivity. Then another algorithm is given to compute the sensitivity of the entire MLP network. Computer simulations are used to verify the derived theoretical formulas. The agreement between theoretical and experimental results is quite good. The sensitivity measure can be used to evaluate the MLP's performance.

Neural network methods for one-to-many multi-valued mapping problems

“…In sensitivity analysis, the significance of a single input feature to the output of a trained neural network is studied by applying that input, while keeping the rest of the inputs fixed and observing the variation of the output to that particular stimuli (see for example [30] and references therein). In the problems investigated in this paper, we do not have a trained neural network, but the index based on the values of 20 stocks in the first problem and in the second problem the average grade based on four subjects or the grade of one subject in relation to three other subjects.…”

Isolating Stock Prices Variation with Neural Networks

“…In sensitivity analysis the significance of a single input feature to the output of a trained neural network is studied by applying that input, while keeping the rest of the inputs fixed and observing how sensitive the output is to that input feature (see for example [11] and references therein). In the problem investigated in this paper, we do not have a trained neural network, but the index based on the values of 20 stocks.…”

Neural network committee-based sensitivity analysis strategy for geotechnical engineering problems

“…Recently, the development of neural network-based sensitivity analysis algorithms is of increasing interest [8][9][10][11][12][13]. In particular, a comprehensive review and comparison of neural network-based sensitivity analysis algorithms was provided [11], in which a conclusion was reached that the partial derivative algorithm [9] and input perturbation algorithm [10] performed relatively better, especially than the algorithms based on the magnitude of weights [8,12,13].…”

“…In particular, a comprehensive review and comparison of neural network-based sensitivity analysis algorithms was provided [11], in which a conclusion was reached that the partial derivative algorithm [9] and input perturbation algorithm [10] performed relatively better, especially than the algorithms based on the magnitude of weights [8,12,13]. Only the following two algorithms will be addressed and later employed in the analysis of strata movement.…”

“…Neural network-based sensitivity analysis in the general application in prediction, classification and regression is becoming a research focus in artificial intelligence [8][9][10][11][12][13]. Among the existing studies, a single optimal neural network from model selection procedure is commonly employed to perform modeling and afterwards sensitivity analysis.…”