A loss function for box-constrained inverses problems

• Autorzy: Yoneda K.
• Języki publikacji: EN

Abstrakty

EN

A loss function is proposed for solving box-constrained inverse problems. Given causality mechanisms between inputs and outputs as smooth functions, an inverse problem demands to adjust the input levels to make the output levels as close as possible to the target values; box-constrained refers to the requirement that all outcome levels remain within their respective permissible intervals. A feasible solution is assumed known, which is often the status quo. We propose a loss function which avoids activation of the constraints. A practical advantage of this approach over the usual weighted least squares is that permissible outcome intervals are required in place of target importance weights, facilitating data acquisition. The proposed loss function is smooth and strictly convex with closed-form gradient and Hessian, permitting Newton family algorithms. The author has not been able to locate in the literature the Gibbs distribution corresponding to the loss function. The loss function is closely related to the generalized matching law in psychology.

Słowa kluczowe

EN

individual behavior; inverse problems; simultaneous equations; optimization

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Decision Making in Manufacturing and Services
• Rocznik: 2008
• Tom: Vol. 2, no. 1-2
• Strony: 79--98
• Opis fizyczny: Bibliogr. [8] poz., wykr.

Twórcy

autor

Yoneda K.

• Fukuoka University Faculty of Economics 8-19-1 Nanakuma, Jounan-ku, Fukuoka, 814-0180 Japan

Bibliografia

• Campbell R.C., Hill R.C., 2006: Imposing Parameter Inequality Restrictions Using the Principle of Maximum Entropy. Journal of Statistical Computation and Simulation 76, 985-1000, see also http://www.bus.lsu.edu/academics/economics/faculty/chill/personal/maxent.htm.
• Golan A., Judge G., Miller D., 1996: Maximum Entropy Econometrics. Wiley.
• Herrnstein R.J., Rachlin H., Laibson D.I., 1997: The Matching Law: Papers in Psychology and Economics. Harvard University Press.
• Layard R., 2006: Happiness : Lessons from a New Science. Penguin Books.
• McCullagh P., Nelder J. A., 1989: Generalized Linear Models, Second Edition. Chapman & Hall.
• Prelec D., January 1984: The Assumptions Underlying the Generalized Matching Law. Journal of the Experimental Analysis of Behavior 41 (1), 101-107.
• Wichers R., 1996: A Theory of Individual Behavior. Academic Press.
• Yoneda K., December 2006: A Parallel to the Least Squares for Positive Inverse Problems. Journal of the Operations Research Society of Japan 49 (4), 279-289.