Neural Networks in Software

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N eural network technology, a form of artificial intelligence (or AI), arose from endeavors to emulate the kind of information processing and decision making that occurs in living organisms. The goal was to model the behavior of neural tissue in living systems by using a computer to implement structures composed of simulated neurons and neural interconnections (synapses). Research on neural networks began in the 1940s on a theoretical level. When computer technology became sophisticated enough to accommodate such research, the study of neural networks and their applications began in earnest. It was not, however, until the mid-to-late 1980s that neural network technology became of interest to the financial community. By 1989, a few vendors of neural network development tools were available, and there was one commercial S&P 500 forecasting system based on this technology (Scientific Consultant Services NexTurn). In the early 199Os, interest peaked, more development tools appeared, but the fervor then waned for reasons discussed later. While it is not within the scope of this book to present a full tutorial on neural network technology, below is a brief discussion to provide basic understanding. Those interested in exploring this subject in greater depth should read our contrbutions to the books Virtual Trading (Lederman and Klein, 1995) and Computerized Trading (Jurik, 1999), in which we also present detailed information on system development using neural networks, as well as our articles in Technical Analysis of Stocks and Commodities (Katz, April 1992; Katz and McCormick, November 1996, November 1997). Neural Networks in Finance and Znvesting (Trippi and Turban, 1993) should also be of interest.
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WHAT ARE NEURAL NETWORKS Neural nerworks (or nets ) are basically building blocks that learn and are useful for pattern recognition, classification, and prediction. They hold special appeal to traders because nets are capable of coping both with probability estimates in uncertain situations and with fuzzy patterns, i.e., those recognizable by eye but difficult to define in software using precise rules; and they have the potential to recognize almost any pattern that exists. Nets can also integrate large amounts of information without becoming stifled by detail and can be made to adapt to changing markets and market conditions. A variety of neural networks are available, differing in terms of their architecture, i.e., the ways in which the simulated neurons are interconnected, the details of how these neurons behave (signal processing behavior or transfer functions ), and the process through which learning takes place. There are a number of popular kinds of neural networks that are of some use to traders: the Kohonen and the Learning Vector Quantization (LVQ) networks, various adaptive resonance networks, and recurrent networks. In this chapter, the most popular and, in many respects, the most useful kind of network is discussed: the feed-forward network. As mentioned above, nets differ in the ways they learn. The system developer plays the role of the neural network s teacher, providing the net with examples to learn from. Some nets employ supervised learning and others unsupervised learning. Supervised learning occurs when the network is taught to produce a correct solution by being shown instances of correct solutions. This is a form of paired-associate learning: The network is presented with pairs of inputs and a desired output; for every set of inputs, it is the task of the net to learn to produce the desired output. Unsupervised learning, on the other hand, involves nets that take the sets of inputs they are given and organize them as they see tit, according to patterns they lind therein. Regardless of the form of learning employed, the main difficulty in developing successful neural network models is in finding and massaging historical data into training examples or facts that highlight relevant patterns so that the nets can learn efficiently and not be put astray or confused; preprocessing the data is an art in itself. The actual process of learning usually involves some mechanism for updating the neural connection weights in response to the training examples. With feedforward architectures, back-propagation, a form of steepest-descent optimization, is often used. Genetic algorithms are also effective. These are very computationally intensive and time-consuming, but generally produce better final results. Feed-Forward Neural Networks A feed-forward network consists of layers of neurons. The input layer, the tirst layer, receives data or inputs from the outside world. The inputs consist of independent variables (e.g., market or indicator variables upon which the system is to
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be based) from which some inference is to be drawn or a prediction is to be made. The input layer is massively connected to tire next layer, which is often called the hidden layer because it has no connections to tire outside world. The outputs of the hidden layer are fed to the next layer, which may be another hidden layer (if it is, the process repeats), or it may be the output layer. Each neuron in the output layer produces an output composed of the predictions, classifications, or decisions made by the network. Networks are usually identified by the number of neurons in each layer: For example, a 10-3-l network is one that has 10 neurons in its first or input layer, 3 neurons in its middle layer, and 1 neuron in its output layer. Networks vary in size, from only a few neurons to thousands, from only three layers to dozens; the size depends on the complexity of the problem. Almost always, a three- or four-layer network suffices. Feed-forward networks (the kind being used in this chapter) implement a particular form of nonlinear multiple regression. The net takes a number of input variables and uses them to predict a target, exactly as in regression. In a standard linear multiple regression, if the goal is to predict cholesterol (the dependent variable or target) on the basis of dietary fat intake and exercise (the independent variables or inputs), the data would be modeled as follows: predicted cholesterol = a + b * fat intake + c * exercise: where a, b, and c represent parameters that would be determined by a statistical procedure. In a least-squares sense, a line, plane, or hyperplane (depending on the number of independent variables) is being fitted to the points in a data space. In the example above, a plane is being fit: The x-axis represents fat intake, tire y-axis is exercise, and the height of the plane at each xy coordinate pair represents predicted cholesterol. When using neural network technology, the two-dimensional plane or ndimensional hyperplane of linear multiple regression is replaced by a smooth ndimensional curved surface characterized by peaks and valleys, ridges and troughs. As an example, let us say there is a given number of input variables and a goal of finding a nonlinear mapping that will provide an output from the network that best fits the target. In the neural network, the goal is achieved via the neurons, the nonlinear elements that are connected to one another. The weights of the comrections are adjusted to fit the surface to the data. The learning algorithm adjusts the weights to get a particular curved surface that best fits the data points. As in a standard multiple regression model, in which the coefficients of the regression are needed to define the slope of the plane or hyperplane, a neural model requires that parameters, in the form of connection weights, be determined so that the particular surface generated (in this case a curved surface with hills and dales) will best fit the data. NEURAL NETWORKS IN TRADING Neural networks had their heyday in the late 1980 and early 1990s. Then the honeymoon ended. What happened Basically, disillusionment set in among traders
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