Neural networks stochastic models

Hidden Markov models (HMMs) are constructed by using concepts such as conditional probability. They are used in a variety of applications, and are classified under a useful class of probabilistic models. HMMs are a special case of neural networks, stochastic networks, and Bayesian networks. The dyad probabilities as a function of reactor monomer composition are given in Table 11.1. The probabilities are calculated using Equations (11.8 11.10). 

Chapter 10 covers another important field with a great overlap with CA neural networks. Beginning with a short historical survey of what is really an independent field, chapter 10 discusses the Hopfield model, stochastic nets, Boltzman machines, and multi-layered perceptrons. 

Bridle, J. S. (1990b). Training stochastic model recognition algorithms as networks can lead to maximum mutual information estimation of parameters. In Advances in Neural Information Processing Systems, vol. 2 (ed. D. S. Touretzky), pp. 211-17. Morgan Kaufmann, San Mateo. 

Several stochastic models, based on mutli-parametric regression, artificial neural networks, Kalman filter and other statistical techniques, were implemented for short-term forecast of air pollution episodes, namely high ozone concentrations (Czech Republic, Hungary, Poland, Slovenia). 

The arrangement can be still more complex. For example, in a class of neural networks called thermodynamic models, each unit can output 0 or 1, and a stochastic function operating on the unit s inputs determines the probability that its output will be 1 (2). 

Artificial Neural Networks (ANNs) have been deemed successful in applications involving classification, identiflcation, pattern recognition, time series forecasting and optimisation. ANNs are distributed information-processing systems composed of many simple computational elements interacting across weighted connections. It was inspired by the architecture of the human brain. The ability of ANNs to model a complex stochastic system could be utilised in risk prediction and decision-making research, especially in areas where multi-variate statistical analysis is carried out. 

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