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Bayesian stopping rule in discrete parameter space with multiple local maxima. (English) Zbl 1463.62245
Summary: The paper presents the stopping rule for random search for Bayesian model-structure estimation by maximising the likelihood function. The inspected maximisation uses random restarts to cope with local maxima in discrete space. The stopping rule, suitable for any maximisation of this type, exploits the probability of finding global maximum implied by the number of local maxima already found. It stops the search when this probability crosses a given threshold. The inspected case represents an important example of the search in a huge space of hypotheses so common in artificial intelligence, machine learning and computer science.
62L15 Optimal stopping in statistics
62F15 Bayesian inference
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[1] Artin, E., The Gamma Function., Holt, Rinehart, Winston, NY 1964
[2] Barndorff-Nielsen, O., Information and Exponential Families in Statistical Theory., Wiley, NY 1978
[3] Berger, J. O., Statistical Decision Theory and Bayesian Analysis., Springer, NY 1985
[4] Bharti, K. K.; Singh, P. K., Hybrid dimension reduction by integrating feature selection with feature extraction method for text clustering., Expert Systems Appl. 42 (2015), 3105-3114
[5] Ferguson, T. S., Who solved the secretary problem?, Statist. Sci. 4 (1989), 3, 282-289
[6] Foss, S.; Korshunov, D.; Zachary, S., An Introduction to Heavy-Tailed and Subexponential Distributions., Springer Science and Business Media, 2013
[7] Horst, R.; Tuy, H., Global Optimization., Springer, 1996
[8] Kárný, M., Algorithms for determining the model structure of a controlled system., Kybernetika 9 (1983), 2, 164-178
[9] Kárný, M.; Böhm, J.; Guy, T. V.; Jirsa, L.; Nagy, I.; Nedoma, P.; Tesař, L., Optimized Bayesian Dynamic Advising: Theory and Algorithms., Springer, 2006
[10] Kárný, M.; Kulhavý, R., Structure determination of regression-type models for adaptive prediction and control., In: Bayesian Analysis of Time Series and Dynamic Models (J. C. Spall, ed.), Marcel Dekker, New York 1988
[11] Knuth, D. E., The Art of Computer Programming, Sorting and Searching., Addison-Wesley, Reading 1973
[12] Lizotte, D. J., Practical Bayesian Optimization., PhD Thesis, Edmonton, Alta 2008
[13] Novovičová, J.; Malík, A., Information-theoretic feature selection algorithms for text classification., In: Proc. of the IJCNN 2005, 16th International Joint Conference on Neural Networks, Montreal 2005, pp. 3272-3277
[14] Peterka, V., Bayesian system identification., In: Trends and Progress in System Identification (P. Eykhoff, ed.), Pergamon Press, Oxford 1981, pp. 239-304
[15] Shahriari, B.; Swersky, K.; Wang, Z.; Adams, R. P.; Freitas, N. de, Taking the human out of the loop: A review of Bayesian optimization., Proc. IEEE 104 (2016), 1, 148-175
[16] Wolpert, D. H.; Macready, W. G., No free lunch theorems for optimization., IEEE Trans. Evolutionary Comput. 1 (1997), 1, 67-82
[17] Zellner, A., An Introduction to Bayesian Inference in Econometrics., J. Wiley, NY 1976
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