Simulation of Human Subjective Judgement with Neural Networks: The Computer Plays the Classifier, the Sommelier and the judge

• Autore: Mario Giaccio/Francesco Romeo
• Carica: Dipartamento di Metodi Quantitativi e Teoria Economia/Instituto di Studi Giuridici
• Pagine: 85-120

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@1. Introduction

@@1.1. Subjective Judgement and the Law

Our research focuses on the computerized simulation of subjective judgement.

Considering the approach that sees judgement as a final result of a complex mental activity, which has the perception of a stimulus¹ as a starting point, we have tried to divide this activity into different steps, as follows:

1. Perception

2. Classification

3. Qualification and Evaluation

4. Judgement

   Perception has been excluded from our research, as it is being studied by experts in pattern recognition as well as widely throughout the world.

   Subjective judgement deals with the application and interpretation of the law from several points of view.

   At the time of law-making, the target Is that of outlining the application range of a legal provision; because of that it Is necessary to give definitionsPage 86 and classifications, which are often conventional and consequently often quixotic or unfair in their outcome, We have chosen the example of mineral waters in trying to analyze the ability of a neural net to induce a new classification, according to the natural features of the waters and, at the same time, to give an exclusive answer according to the assessment of the law.

   Subjective judgement also plays a relevant role at the time when the law is applied: often the law itself requests it. Our examples relate to attributing the quality trade mark to wines² and the trade mark «extra virgin olive oil» to oils³. The goal is to verify the ability of a neural net to simulate a human like/dislike choice reaching a standardization of it that will ensure a more certain application of the law.

   With regard to legal interpretation, subjective judgement deals with all that is not definite and-explicit in the law and, nevertheless necessary for giving an equitable decision representing the full legal content. We have chosen the example of civil liability resulting from a car accident. The goal is to test the ability of neural nets to self organize a suitable judgement measure that can not only be an application of legal provisions but also a right or reasonable judgement for all analogous cases that have not been programmed or could not be foreseen.

   @@2.1. Neural Networks

   A neural network is a parallel distributed information processing structure in the form of a directed graph [a geometrical object consisting of a set of points (called nodes) along with a set of directed line segments (called links) between them]

   ⁴ [Fig. 1].

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   [ GRAPHICS ARE NOT INCLUDED ]

   This definition is created in such a way that it adapts itself to- every neural network; however, it does not gather each one's characteristics. Neural networks were developed on the basis of research into artificial intelligence, whose birth goes back to 1956 to the Darmouth Summer Research Project on Artificial Intelligence, following a low level approach. In the structural and planning stages, this approach already tends to simulate the human brain, in the neuron-synapsis structure, assuming the ability of the network to build and self-organize an intelligent vision of the world around it. This branch of AI research has had, up to recent years, less luck than the «high level» approach that tends to insert an already structured representation of the world surrounding it in a structure, formed independently of every comparison with the human brain, in such a way that it simulates intelligent behaviour in the computer. It is possible to state that interest in neural networks, after the initial results, has developed with the understanding of the limitations cf expert systems, the fortunate outcome of a branch of AI. The first attempts were the Perception by F. Rosenblatt (1957), and ADALINE and MADALINE (Multiple ADAptive LINear Elements) by B, Widrow and M. Hoff (1959) mcdels, leading up to the studies by Hopfield, Grossberg, Mc Clelland, Rumelhart. Sejnowski etc, who, from 1982 up to now, have represented the success of these research projects. Due to the variety of approaches, it is nor possible to describe the various models further- As theirPage 88 functions and possible application domains are quite different, we will, therefore, limit ourselves to describing the model we have used, which is the back-propagation model developed by Rumelhart and McClelland⁵.

   The nodes are the processing elements (pe) that can be linked between themselves with a any number of connections in both the input and output. Every processing element possesses a local memory and a transfer function that operates on the said memory producing the output signal. The PE produces the output signal only if a certain threshold level of input signal is exceeded. The output has a value which is the same for every output connection. At every input a relative weight is assigned that is indicative to the importance of the connection. The output will be given by the summation of the inputs multiplied by the weights. The operation performed by the processor is essentially:

   [ IT DOES NOT INCLUDE FORMULATES ]

   where xj are the input values, yi are the output values, Wij are the weights on the connections Ti are the threshold values and f is the answering function that varies in a continuous interval (0.1). Various functions are related to this basic structure that allow the node to modify itself depending on the input signal. The most important are:

1. The transfer function: it works and modifies the local memory and the input signals and produces the output of the node; as generally it is not linear, we have used a sigmoid function. The puipose of this function is to give not simply a proportional answer to the input signal, This characteristic is important because it pennits the network to adapt itself to the cases where the separation between the data is not distinct which is the majority of cases.

2. The learning function; it has the role of modifying the weights of every connection. By means of this function the connection is strengthened if it has supplied or operated for an exact answer, it is weakened in the opposite case.

   The possibility of adapting its own configuration depending on the exactness of the answer allows the neural network to learn. The model that we have used propagates the error of the output backwards in respect to the exact data, for this reason it is called the back-propagation model, therefore adapting the configuration of the weights in such a way that it inhibits those that have contributed to the error and stimulates the others.

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   This function, called the delta rule, operates by reducing the difference between the desired value of the output and the value obtained by every node in a continuous way.

   The neural networks are attributed the capacity of adapting, of learning and reacting to stimulus, of self organizing, of inducing, generalizing and extrapolating on the basis of several examples, more than of deducing or operating in a logically determined way on the basis of a program. For these properties, the most diffuse field of research and application is where the input data is presented in a non logically defined or definable way, or also where the data to be processed are shown as fuzzy or not perfectly defined, It happens with pattern recognition or recognition of complex or disorganized structures. It also happens in the understanding of spoken language and, in general, in all that concerns the simulation of human senses. A great success was achieved with networks for military use based on the recognition of military targets by missiles, projectiles etc., on the analysis of images received by satellites and, similarly, on the analysis and classification of radar signals. Some research projects still in course are verifying the use of networks in the meteorological sector, in the location of mines and deposits - in particular, in the oil sector - in the quality control of goods, and in all sectors regarding robotics, etc.

   @@1.3. The Procedure Used

   The work can be carried out with a hardware or a software simulation, We have used the software Neuralworks Explorer II in the back-propagation mode and a personal computer with an Intel 486 processor. As a transfer function, we have used the same sigmoid for every network. The networks were, therefore, trained for 10,000, 100,000, 500,000, 1,000,000 and 2,000,000 cycles depending on the reply to each of these.

   @2. Classification

   @@2.1. Foreword

   The most common⁶ procedures we use for reaching an acceptable description of natural phenomena normally include the following: the mor-Page 90phological method, the classifying method, measuring, and statistical methods. Such descriptive methods, together with the experimental method and the construction of models, are included in the modern subdivision of scientific methods in general⁷.

   The interpretation of the reality that surrounds us, in both natural and social sciences, is often based on the classification of available empirical information. The formulation of many research hypotheses, in order to study various phenomena, can often be changed according to how information is classified. In some cases, the choice of a classification model plays a central role, enabling the interpretation of phenomena. Therefore, classification can be considered, in the field of descriptive methods, the first stage of developing judgements and measures. Furthermore, the new mathematical and statistical procedures used in classifying have allowed this branch of scientific methodology to evolve towards a modern systematics. Classification problems appeared together with the growth of knowledge arising out of the observation of nature and together with the arrival of those problems linked to the «industrial» activity of man: manufactured products, traded goods, etc, showing this double relation to both scientific research (systematic of living beings, of the mineral world, etc) and practical or economical needs (concerning...