Neural network uncertainty assessment using Bayesian statistics with application to remote sensing: 3. Network Jacobians

International audienceUsed for regression fitting, neural network (NN) models can be used effectively to represent highly nonlinear, multivariate functions. In this situation, most emphasis has been on estimating the output errors, but almost no attention has been given to errors associated with the internal structure of the NN model. The complex relationships linking the inputs to the outputs inside the network are the essence of the model and assessing their physical meaning makes all the difference between a "black box" model with small output errors and a physically meaningful model that will provide insight on the problem and will have better generalization properties. Such dependency structures can, for example, be described by the NN Jacobians: they indicate the sensitivity of one output with respect to the inputs of the model. Estimating these Jacobians is essential for many other applications as well. We use a new method of uncertainty estimate developed in the work of [2004] to investigate the robustness of the quantities that characterize the NN structure. A regularization strategy based on principal component analysis is proposed to suppress the multicolinearities that are a major concern when analyzing the internal structure of such a model. The theory is applied to the remote sensing application already presented in the work of [2004] and [2004]