Predictive decision making under risk and uncertainty: A support vector machines model

Al-Rawabdeh, Wasfi A.; Dalalah, Doraid

RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 3, pp. 639-667.

In this paper, a decision making model using support vector machine (SVM) approach is presented. Here, human attitude towards risk and uncertainty is identified via optimizing SVM certainty classification model. In particular, individuals are given different pairs of gambles in order to reveal their preference. Unlike traditional methods used to estimate the utility function through direct inquiry of the certainty equivalents, pair-wise comparisons are used here in the training process to predict human preferences and to compute the utility parameters. The presented study is characterized by first, the use of SVM in the field of decision making to classify individuals’ choices, second, it uses such model to search for the optimal utility parameters, third, the model can be used to guide the decision makers towards better decisions. In contrast to existing utility models, the SVM utility approach is characterized by its tolerance to misclassification in the training and testing data sets which makes it cope with the existing violations such as the common consequence, common ratio and violation of betweenness in the utility theory. To demonstrate the merits of the model, different data sets were used from well known literature studies and new conducted surveys that elicit individual preferences. The data is split into training and testing sets. The results demonstrated a notable consistency in the computed utility parameters and remarkable predictions without the need to strict certainty equivalent estimation. The model can be beneficial in predictive decision making under risk and uncertainty.

Classification : 90Cxx, 62Cxx, 80Mxx, 60Gxx
Mots clés : Decision making, expected utility theory, support vector machines, optimization

M. Allais, Le Comportement de l’Homme Rationnel devant le Risque: Critique des Postulats et Axiomes de l’École Américaine. Econometrica 21 (1953) 503–546. | DOI | MR | Zbl

P.R. Blavatskyy, Violations of Betweenness or Random Errors? Econ. Lett. 91 (2006) 34–38. | DOI | Zbl

P.R. Blavatskyy, Stochastic Expected Utility Theory. J. Risk Uncertain 34 (2007) 259–286. | DOI | Zbl

B.E. Boser, I.M. Guyon and V.N. Vapnik, A training algorithm for optimal margin classifiers. In Proc. of the Fifth Annual ACM Workshop on Computational Learning Theory. New York, NY (1992).

D. Butler and G. Loomes, Imprecision as an account of violations of independence and betweenness. J. Econ. Behav. Organiz. 80 (2011) 511–522. | DOI

M. Colyvan, No Expectations. Mind 116 (2006) 695–702. | DOI

M. Colyvan, Relative Expectation Theory. J. Philos. 105 (2008) 37–44. | DOI

C. Cortes and V. Vapnik, Support-vector network. Mach. Learn. 20 (1995) 273–297. | DOI | Zbl

D. Dalalah, W.A. Al-Rawabdeh and H. Alshraideh, The beta stochastic utility ($\beta$-SU). Stoch. Anal. Appl. 34 (2016) 456–482. | DOI | MR | Zbl

K. Easwaran, Strong and Weak Expectations. Mind 117 (2008) 633–641. | DOI | MR

K. Easwaran, Regularity and Hyperreal Credences. Philos. Rev. 123 (2014) 1–41. | DOI

U.W. Elke, A.-R.E. Blais and N.E. Betz, A Domain-specific Risk-attitude Scale: Measuring Risk Perceptions and Risk Behaviors. J. Behav. Decis. Making 15 (2002) 263–290. | DOI

T. Fine, Evaluating the Pasadena, Altadena, and St Petersburg Gambles. Mind 117 (2008) 613–632. | DOI | MR

T. Hastie, R. Tibshirani and J. Friedman, The elements of statistical learning: Data mining inference and prediction, 2nd edition. Springer, New York (2009). | MR | Zbl

C.A. Holt and S.K. Laury, Risk aversion and incentive effects. Am. Econ. Rev. 92 (2002) 1644–1655. | DOI

D. Kahneman and A. Tversky, Judgment Under Uncertainty: Heuristics and Biases. Sci. Mag. 185 (1974) 1124–1131.

S.K. Laury and C.A. Holt, Further reflections on prospect theory. Exp. Econ. 12 (2008) 405–40.

Y. Lee, Y. Lin and G. Wahba, Multicategory support vector machines, theory, and application to the classification of microarray data and satellite radiance data. J. Am. Stat. Assoc. 99 (2004) 67–81. | DOI | MR | Zbl

G. Loomes and R. Sugden, Testing Different Stochastic Specifications of Risky Choice. Economica 65 (1998) 581–598. | DOI

J.M. Machina, Choice under Uncertainty: Problems Solved and Unsolved. J. Econ. Perspect. 1 (1987) 121–154. | DOI

J. Marron, Distance-weighted discrimination. J. Am. Stat. Assoc. 102 (2007) 1267–1271. | DOI | MR | Zbl

X. Qiao, H.H. Zhang, Y. Liu, M.J. Todd and J.S. Marron, Asymptotic properties of distance-weighted discrimination. J. Am. Stat. Assoc. 105 (2010) 401–414. | DOI | MR

X. Shen, G.C. Tseng, X. Zhang and W.H. Wong, On $\psi$-Learning. J. Am. Stat. Assoc. 98 (2003) 724–734. | MR | Zbl

M. Siamak and A.K.J. Suykens, Learning solutions to partial differential equations using LS-SVM. Neurocomputing 159 (2015) 105–116. | DOI

C. Starmer, Developments in Non-Expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk. J. Econ. Literature 38 (2000) 332–382. | DOI

M. Thalos and O. Richardson, Capitalization in the St. Petersburg game: Why statistical distributions matter. Politics Philosophy Economics (2013) 1–22.

A. Tversky and D. Kahneman, Advances in Prospect Theory: Cumulative Representation of Uncertainty. J. Risk Uncertain 5 (1992) 297–323. | DOI | Zbl

Zhigang Wang, Zengshum Zhao, Shifeng Weng and Changshui Zhang, Solving one-class problem with outlier examples by SVM. Neurocomputing 149 (2015) 100–105. | DOI

G. Wu, J. Zhang and R. Gonzalez, Decision under Risk. In The Blackwell Handbook of Judgment and Decision Making, edited by D. Koehler and N. Harvey. Blackwell, Oxford, England (2004) 399–423.

J. Zhu and T. Hastie, Kernel Logistic Regression and the Import Vector Machine. J. Comput. Graph. Stat. 14 (2005) 185–205. | DOI | MR

J. Zhu, H. Zou, S. Rosset, T. Hastie, Multi-class adaboost. Stat. Interface 2 (2009) 349–360. | DOI | MR | Zbl

Li Ziqiang, Mingtian Zhou, Lijia Xu, Hao Lin, Haibo Pu, Training sparse SVM on the core sets of fitting-planes. Neurocomputing 130 (2014) 20–27. | DOI