Titlebook: Neural Networks for Conditional Probability Estimation; Forecasting Beyond P Dirk Husmeier Book 1999 Springer-Verlag London Limited 1999 al

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Book 1999ective is to predict the future value of some entity of interest on the basis of a time series of past measurements or observations. Typical training schemes aim to minimise the sum of squared deviations between predicted and actual values (the ‘targets‘), by which, ideally, the network learns the c

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A Universal Approximator Network for Predicting Conditional Probability Densities, networks are presented, and their relation to a stochastic kernel expansion is noted. The chapter concludes with a comparison between these models and several relevant alternative approaches which have recently been introduced to the neural network community.

ALB

A Maximum Likelihood Training Scheme,s shown to suffer from considerable inherent convergence problems due to large curvature variations of the error surface. A simple rectification scheme based on a curvature-based shape modification of E is presented.

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Demonstration: Committees of Networks Trained with Different Regularisation Schemes,heme is found to lead to superior results. However, when using network committees, under-regularisation can be advantageous, since it leads to a larger model diversity, as a result of which a more substantial decrease of the generalisation ‘error’ can be achieved.

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Introduction, weather, or the economy, it is not possible to solve the equations of dynamics explicitly and to keep track of motion in the high dimensional state space. In these cases model-based forecasting becomes impossible and calls for a different prediction paradigm.

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Benchmark Problems,l potential subject to Brownian dynamics. The resulting time series shows fast oscillation around one of two metastable states and occasional phase transitions between these two states. As a consequence of the latter, long-term predictions require a model that can capture bimodality.

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Summary,sons discussed in Chapter 1, the distribution is likely to be distorted and may be multimodal. This suggests that, in general, it is not sufficient to train a network to predict only a single value, but that the complete probability distribution of the target conditional on the input vector should be modelled.