Elicitation of Decisionmaker Preference By

Artificial Neural NetworksZHUANG CHUANLI, REN JINZHENG

College of Economics & Management,China Agricultural University,100083,Beijing P.R. Chinazhuangchuanli( l 63.com

Abstract-The classical elicitation methods are not robustwhen decisionmaker distort or misperceive probabilities. So,which makes it difficult for using the methods in certainapplications. This paper presents a new model to elicit thedecisionmaker preferences by artificial neural networks(ANNs). This model simulating human thought and cognition ismore consistent with the real utility of a decisionmaker. A BPneural network of 3-layers was designed to elicit adecisionmaker utility, and the result was superior to classicalelicitation method (i.e. CE). In a word, ANNs present a newmethod and insight for us to solve the utility elicitationquestion.

I. INTRODUCTION

Preference and utility are two fundamental items ineconomic and management science. Preference is widelyaccepted to describe the satisfaction that someone receivesfrom consuming commodities or from the observed choicedecisions [1]. The relation between utilities and preference isgiven by defming utility as the measurement of strength orintensity of a decisionmaker's preferences [2]. Utilityelicitation is the procedure of extracting necessarypreference or utility information from a decisionmaker [3].The procedure serves a crucial role in developing a decisionsupport system.Many researches had been conducted in this area. Some

utility elicitation procedures, which goal was to build autilities function, were designed. Most of them arechoice-based which allows inferring the economiccharacteristics of an individual from the observed choicedecisions of this decisionmaker. In choice under risk [4] animportant characteristic of an individual is his or her utilityof outcomes [. One of the first attempts to elicit adecisionmaker's utility function u: R - R can be found inRamsey [6] Classical non-parametric elicitation methodssuch as certainty equivalent (CE) and probability equivalent(PE) methods [7] allow a researcher to infer the utilityfunction of an individual without assuming a specificparametric form and without excluding the heterogeneity in

GAO BO, FU ZETIAN*College of Engineering, China AgriculturalUniversity, 100083 Beijing P.R. ChinaKey Laboratories ofModem Precision

Agriculture System Integration,Ministry of Education,

100083, Beijing P.R. China

the decisionmaker's preferences. Unfortunately, the classicalelicitation methods are not robust when decisionmakerdistort or misperceive probabilities. So, which makes itdifficult for using the methods in certain applications.

This paper presents a new model to elicit the userpreferences by artificial neural networks (ANNs). Thismodel removes the barriers that classical elicitation methodsalways adopt linear or few non-linear functions thatindicated an individual utility of outcomes. The ANNsutility elicitation not only can simulate human thought andcognition, which results are more consistent with the realutility of a decisionmaker, but also modify model by newcases.

This paper is organized as fellow. In section 2, wepresented the Synopsis of artificial neural networks.Section 3 explained the new method of utility elicitation,especially focused on data analysis, model design andparameters setup. Section 4 described the experiment andthe results of the new method. Section 5 concludes ourdescribed research.

II. ANNS & PERFORMANCE

A. Synopsis ofANNs

The science of ANN began in the early 1950s as an

PE

Y=f(x)

Fig 1. Neuron model

attempt to mathematically model the human brain. ANN,

0-7803-9422-4/05/$20.00 C2005 IEEE1699

also called 'neural network' , 'parallel distributedprocessing' , and 'connectionist' models, developed outof the areas of artificial intelligence and cognitive science intheir attempts to model the human brain and its learningprocess.J8' The ANN model has a fundamental processingunit called a neuron. Fig. 1 shows a conceptual model of the

f(4

i h

0 x

Fig 2. Shape ofthe sigmoid function

neuron, which receives several inputs through connectionscalled synapses. The incoming activations are multiplied bythe synaptic weights and summed up. The outgoingactivation is determined by applying a threshold function tothe summation. The neuron has only one outgoing activationvalue although it might have several connections to theother neuron. The threshold function is a non-linear function

input output

input hidden outputlayer(i) layer(J) layer(k)

Fig 3. Diagram ofthe back-propagation model

input data. For inputs that have not been experienced orpartially damaged, distorted or mixed with noise,appropriate outputs are generated based on its internalknowledge stored in connection weights.

Back-propagation learning chosen as the 'training'algorithm in this paper is the name of a supervised trainingalgorithm by teacher's (known) data. It is necessary to haveboth input and output data to train the network. The basicconcept of the back-propagation learning is shown in Fig. 3,where first, the input patterns of each node are provided atthe input layer; then, this signal is converted at each nodeand transferred to the hidden layer; and finally, the signalgenerate outputs in the output layer. The output values arecompared to the target values and the connection weights(wji , wA, ) are adjusted in the direction that provides lessdifference between two values. This adjustment is backpropagated from the upper layers to the lower layers, whichresults in the adjustment of the connection weights in thelower layers.

Using the ANN model in building system control has thefollowing advantages:

First, less knowledge, tests, etc. are required to determineinput/output relations, whereas even a quadratic systemrequires a great number of tests and simulations in amathematical model. In the case of the ANN, the above istrue even in the modeling of non-linear multi-variablesystems.

Second, deviations from the optimal value or noisesignals in on-line learning do not cause significantperformance degradation. With mathematical models, usingnumerouis variables can create difficulties in calculation.

Third, the ANN models input and output through learningbased on prior experience data relations so that no additionalinput data are needed for the control object. Also, once thegiven network has finished learning, the response isimproved, because the control inputs can be obtained in ashort amount of time. With mathematical models, it isdifficult to create a model exactly the same as the buildingin question for application to an actual building, and it isalso difficult to model relations between various input andoutput variables, because it takes a long time to performsimulations.

that decides the output of a particular neuron [9,10]. Fig. 2shows a popular activation function, called the logistic orsigmoid function.ANNs are collections of small individual interconnected

processing units with weights associated with eachconnection. Learning is the first necessary step in inducingintelligence to neural networks. In learning, ANN are'taught' by presenting sets ofpatterns to be 'learned'

and autonomously adjusts the connection weights amongprocessing units according to imposed learning rules andthereby, obtains unique knowledge from the data. Thelearned neural network generates accurate outputs for the

B. ANNs Performance

In this study, two statistical criteria were adopted to selectthe desired optimal network model. The statistical criteriaconsist of average squared of error (ASE) and coefficient ofdetermination (R2). They are given by

n

L(Xi Xi)2ASE= i=1 .... (1)

n

1700

-----------T-1 -

n

E(Xi - Xi

i=l

A~~~~~~

where Xi and Xi are respectively, the actual and

predicted value of flow, (X is the mean of X, values and

n is the total number of data sets. The R2 statisticmeasures the linear correlation between the actual andpredicted flows values. The ASE statistic measures are usedto quantify the error between observed and predicted values.The optimal value for R2 is equal to 1.0 and for ASE istrend to 0.0.

IIl. METHODOLOGY AND MODEL

A. Data analysis

In this study, we collected information by questionnaire.Question in questionnaire are similar with the question inclassical Certainty Equivalent (CE) Method. In CE method,a two-outcome lottery is denoted by (x, p; z) that assignsprobability p to outcome x and probability I - p to outcomez. This method can elicit utilities by obtaining indifferencepoints from an informant. The analyst asks the informant tocompare a lottery (x, p; z) with a certain outcome. Theanalyst varies the certain outcome until the informantreveals indifference between the certain outcome y and thelottery (x, p; z). So that, many indifference points will beobtained.

During the investigation, we selected 6 informants, anddistributed 3 copies of our risk decision utility questionnaireat three times. Each copy had 10 questions that were dividedinto three types. To keep it simple, we assumed z =0 in allthree type questions. The first type, we fixed the x=100 andvaried the p from 0 to 1. The second, p were fixed on 0.1

outp

x

p

input hiddenlayer layer

outputlayer

Fig 4 Diagram of the back-propagation model

u

and varies x from 0 to 100. The third, p were fixed on a 0.9and varies x from 0 to 100. But to avoid informant disturbedby recency effects, 10 questions are random arrayed todisplay in three questionnaires. The questionnaires we havedistributed add up to 18 in number and have received 18feedbacks. All ofthem are effective.The answers of feedback questionnaires were

pre-processed as the form (x, p, z). In term of adopting theANNs utility elicitation model and demonstrating theefficiency of the new model, 20 of 30 data correspondingwith every informant were selected stochastically as trainingsets, and rest as testing sets.

B. Model design

The ANNs have much different architecture and the mostpopular type of neural network is the back propagationneural network (BP). BP works well for pattern matchingand for trend analysis. The BP can learn many differentoutput patterns simultaneously with dramatic accuracy. Aconventional BP uses three layers of nodes, the input layer,the hidden layer and output layer. According to aboveprinciple and the practices problem, the new modelsarchitecture in this study is as fig 4. The input patternconsists of two input neurons (x, p). The hidden layerconsists of 2118 hidden neurons. The output pattern consistsof only one output neuron (u).

C. Parameter setting

Because the parameter setup has a heavy influence on theaccuracy of BP' results, we should adjust the parameter ofBP neural networks until the result reach the satisfaction ofanalyzer.

There are two transfer functions and three trainingparameters associated with networks. Transfer functionscalculate a layer's output vector (or matrix) A, given its netinput vector (or matrix) N. The only constraint on therelationship between the output and net input is that theoutput must have the same dimensions as the input. Thethree training parameter include learning rate, epoch andgoal. The learning rate is multiplied times the negative ofthe gradient to determine the changes to the weights andbiases. The other two parameters determine when thetraining stops. The training stops if the number of iterationsexceeds epochs, if the performance fimction drops belowgoal.

After hundred times experiment, the key parameters ofthe BP Artificial neural network elicitation model were setup as following: the two transfer function are purelin

2(f(x) =x ) and tansig (f(x) = 2 -1 ), and the

learning rate was 0.9 and the training epoch set 2500 and thegoal was 0.001.

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I-* RTraining ASE --Testing ASE

The new model was performed in Matlab toolbox. Thegoal was reached when the epochs were 117 (fig. 5), and theANNs were trained successfully. Then the test data wasinputted to demonstrate the ability of the trained net. Thecorresponding accuracy measures of this network model ontesting and training data were given in the following table(Table 1 ).

SN_S E&?8?8vsBxBBiit-&?i- S'+....................................................g;::2:^.... 2:

70

60

50

"I 40

30

20

10

01 2 3 4 5 6

Informant

(a)

_ Training R x---Testing R

Fig.5 the perfonnance of training networksGenerally, accuracy measures on training data were better

than those on testing data.

Table 1. Statistical accuracy measures of this networkmodel at testing and training phase

Training set Testing setASE R ASE

Person 1 0.1 1 27.5 0.991Person 2 0.1 1 38.1 0.989Person 3 0.1 1 20.4 0.993Person 4 0.1 1 30.2 0.990Person 5 0.1 1 21.7 0.993Person 6 0.1 1 62.5 0.987

The comparison between the utility and actual values attraining and testing phases showed excellent agreement withthe R2. The difference accuracy between training set andtesting set are also showed intuitionally in fig.6.

1. 005

1

0. 995c" 9

0.99

0. 985

0.98

.- . . . . .--

1 2 3 4 5 6Informant

(b)

Fig 6. Comparison between the actual andANNs utility elicitation values

In order to evaluate the performance of the ANN, theclassical CE method was applied with the same data setsused in the ANN model. The R2 values and ASE values ofCE and ANN models are presented in table 2 and fig.7.Apparently, the ANN approach gave much realer utility thanthe traditional method.

Table 2 Comparison ofASE and R2 betweenANNs and CE models

Training set I Testing setsAME R2 AME R2

CE 116.3 0.901 147.2 0.867ANN 0.1 1 33.4 0.991

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IV. RESULTS AND DISCUSSIONS

[8] Xu Dong, Wu Zheng, Analysis and design for ANN based on

|160 MATLAB6.x. Xi an: Xidian University Press, 2002.147_ 2 [9] J. Hertz, A. Krogh, R. Palmer, Introduction to the Theory of Neural140 Computation, Addison-Wesley, Reading, MA, 1995.

l 116. 3 -[10] G. Hinton, "Connectionist learning procedures", Artif Intell., vol 40,120 pp. 185-234, 1989.

100

¢80 E - _ _ 11 *CE Method2*ANN Method

60

40

20

Training set Testing set

Fig 7. Comparison between ANNs and CE method

V. CONCLUSION

A new utility elicitation model was developed based onartificial neural networks in this paper. The result shows thatthe BP neural networks can simulate human thought andcognition processing to elicit the preference and learn theutility of an individual. Compared with classical utilityelicitation model, the BP neural networks model is goodcapability to model utility elicitation process. It alsoindicates that ANNs are useful and powerful tools to handlecomplex problems in economic activity.

But, because of the parameter in this new modelimportance, the researcher needs more time to look for theright value of parameter. Other question is that the numberof data has an important influence on the accuracy of result.Still, ANNs present a new method and insight for us to solvethe utility elicitation question.

REFERENCES

[1] P.H.M.P. Roelofsma, M.C. Schut, "Preference Elicitation withoutNumbers," AAMAS'04, 2004, pp.103-1 10, New York USA.

[2] J. Dyer and R. Sarin, "Relative risk aversion," Management Science,vol 28, pp. 875-886, 1982.

[3] C. Boutilier, "A POMDP formulation of preference elicitationproblems," Proceedings of the Eighteenth National Conference onArtificial Intelligence and Fourteenth Conference on InnovativeApplications ofArtificial Intelligence (AAAI/IAAI-02), where, 2002, pp.239-246.

[4] Knight, F.H, Risk, uncertainty and profit, Houghton Mifflin: BostonPress, 1921.

[5] Von Neumann, J. and 0. Morgenstern, Theory ofgames and economicbehavior, Princeton: Princeton University Press, 1944.

[6] Ramsey, F, "Truth and probability" in "The foundations ofmathematics and other logical essays ", pp. 156-198, London:Routledge and Kegan Paul, 1931.

[7] Farquhar, P. Utility Assessment Methods, Management Science, vol 30,pp. 1283-1300, 1984.

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