Neural Networks for Conditional Probability Estimation: Forecasting Beyond Point Predictions (Perspectives in Neural Computing)

Dirk Husmeier

ISBN 10: 1852330953 / ISBN 13: 9781852330958

Published by Springer 2013-10-04, 2013

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Seller Inventory # 6666-IUK-9781852330958

Bibliographic Details

Title: Neural Networks for Conditional Probability ...

Publisher: Springer 2013-10-04

Publication Date: 2013

Binding: Paperback

Condition: New

About this title

Synopsis:

Conventional applications of neural networks usually predict a single value as a function of given inputs. In forecasting, for example, a standard objective 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 conditional mean of the target given the input. If the underlying conditional distribution is Gaus­ sian or at least unimodal, this may be a satisfactory approach. However, for a multimodal distribution, the conditional mean does not capture the relevant features of the system, and the prediction performance will, in general, be very poor. This calls for a more powerful and sophisticated model, which can learn the whole conditional probability distribution. Chapter 1 demonstrates that even for a deterministic system and 'be­ nign' Gaussian observational noise, the conditional distribution of a future observation, conditional on a set of past observations, can become strongly skewed and multimodal. In Chapter 2, a general neural network structure for modelling conditional probability densities is derived, and it is shown that a universal approximator for this extended task requires at least two hidden layers. A training scheme is developed from a maximum likelihood approach in Chapter 3, and the performance ofthis method is demonstrated on three stochastic time series in chapters 4 and 5.

Synopsis:

Using two alternative approaches, the GM network and the GM-RVFL model, this study of the applications of neural networks includes a case study of the prediction of housing prices in the Boston metropolitan area, and examines the required modifications to standard approaches.