Learning internal representations by error propagation
Parallel distributed processing: explorations in the microstructure of cognition, vol. 1
Advances in neural information processing systems 2
Neural networks and the bias/variance dilemma
Neural Computation
A practical Bayesian framework for backpropagation networks
Neural Computation
The nature of statistical learning theory
The nature of statistical learning theory
Neural networks for pattern recognition
Neural networks for pattern recognition
NETLAB: algorithms for pattern recognition
NETLAB: algorithms for pattern recognition
Bayesian Learning for Neural Networks
Bayesian Learning for Neural Networks
Introduction to the Theory of Neural Computation
Introduction to the Theory of Neural Computation
Neural Network Modelling with Input Uncertainty: Theory and Application
Journal of VLSI Signal Processing Systems
Mlps (mono layer polynomials and multi layer perceptrons) for nonlinear modeling
The Journal of Machine Learning Research
The “weight smoothing” regularization of MLP for Jacobian stabilization
IEEE Transactions on Neural Networks
Neural Networks - 2006 special issue: Earth sciences and environmental applications of computational intelligence
Estimating per-pixel thematic uncertainty in remote sensing classifications
International Journal of Remote Sensing
Hi-index | 0.00 |
Neural network (NN) techniques have proved successful for many regression problems, in particular for remote sensing; however, uncertainty estimates are rarely provided. In this article, a Bayesian technique to evaluate uncertainties of the NN parameters (i.e., synaptic weights) is first presented. In contrast to more traditional approaches based on point estimation of the NN weights, we assess uncertainties on such estimates to monitor the robustness of the NN model. These theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature, microwave surface emissivities, and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land.The weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs (i.e., error bars and correlation structure of these errors). Such quantities are very important for evaluating any application of an NN model.The uncertainties on the NN Jacobians are then considered in the third part of this article. Used for regression fitting, NN models can be used effectively to represent highly nonlinear, multivariate functions. In this situation, most emphasis is put on estimating the output errors, but almost no attention has been given to errors associated with the internal structure of the regression model. The complex structure of dependency inside the NN is the essence of the model, and assessing its quality, coherency, and physical character makes all the difference between a blackbox model with small output errors and a reliable, robust, and physically coherent model. Such dependency structures are described to the first order by the NN Jacobians: they indicate the sensitivity of one output with respect to the inputs of the model for given input data. We use a Monte Carlo integration procedure to estimate the robustness of the NN Jacobians. A regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these Jacobians robust and physically meaningful.