## Publication Abstracts

### Aires et al. 2004

Aires, F., C. Prigent, and **16**, 2415-2458.

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 neural network weights, we assess uncertainties on such estimates to monitor the robustness of the neural network 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 a NN model.

The uncertainties on the NN Jacobians are then considered in the third part of this paper. 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 "black-box" 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 a 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 multi-collinearities in order to make these Jacobians robust and physically meaningful.

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#### BibTeX Citation

@article{ai04100j, author={Aires, F. and Prigent, C. and Rossow, W. B.}, title={Neural network uncertainty assessment using Bayesian statistics: A remote sensing application}, year={2004}, journal={Neural Comput.}, volume={16}, pages={2415--2458}, }

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#### RIS Citation

TY - JOUR ID - ai04100j AU - Aires, F. AU - Prigent, C. AU - Rossow, W. B. PY - 2004 TI - Neural network uncertainty assessment using Bayesian statistics: A remote sensing application JA - Neural Comput. VL - 16 SP - 2415 EP - 2458 ER -

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