2 Neural Networks

Artificial neural networks derive their origins from biological neural networks. They are systems of parallel and distributed processing that simulate the basic operating principles of the biological brain. Sometimes they are referred to in the literature as machine learning algorithms. The biological brain in its basic structure is a network of neural cells (neurons) attached through connections that have the ability to adjust the power of the electrical pulse that runs through them (synapses). The external stimulus in the form of an electrical pulse is transmitted as information through synapses to the neurons, where it is processed, and eventually, an output response of the network is produced. The information is encoded as “knowledge” through continuous updating of the existing synapses between neurons.

In this book we treat neural networks as the eminent expression of nonparametric regression. Nonparametric regression is a very powerful approach, especially for financial applications. Neural networks can approximate any unknown nonlinear function and are generally less sensitive than classical approaches to assumptions about the error term; hence, they can perform well in the presence of noise, chaotic sections, and fat tails of probability distributions.

The basic aspects of neural networks are presented below. More precisely, the usual training algorithm and network structures are presented. In addition, a geometric explanation of the backpropagation ...

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