Reliable estimation of a neural network's domain of validity through interval analysis based inversion

Reliable estimation of a neural network's domain of validity is important for a number of reasons such as assessing its ability to cope with a given problem, evaluating the consistency of its generalization etc. In this paper we introduce a new approach to estimate the domain of validity of a neural network based on Set Inversion Via Interval Analysis (SIVIA), the methodology established by Jaulin and Walter [1]. This approach was originally introduced in order to solve nonlinear parameter estimation problems in a bounded error context and proved to be effective in tackling several types of problems dealing with nonlinear systems analysis. The dependence of a neural network output on the pattern data is a nonlinear function and hence derivation of the impact of the input data to the neural network function can be addressed as a nonlinear parameter estimation problem that can be tackled by SIVIA. We present concrete application examples and show how the proposed method allows to delimit the domain of validity of a trained neural network. We discuss advantages, pitfalls and potential improvements offered to neural networks.