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Keywords:
global maximum; model structure; Bayesian estimation
global maximum; model structure; Bayesian estimation
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.
References:
[1] Artin, E.: The Gamma Function. Holt, Rinehart, Winston, NY 1964. MR 0165148
[2] Barndorff-Nielsen, O.: Information and Exponential Families in Statistical Theory. Wiley, NY 1978. DOI 10.1002/9781118857281 | MR 0489333 | Zbl 1288.62007
[3] Berger, J. O.: Statistical Decision Theory and Bayesian Analysis. Springer, NY 1985. DOI 10.1007/978-1-4757-4286-2 | MR 0804611
[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. DOI 10.1016/j.eswa.2014.11.038
[5] Ferguson, T. S.: Who solved the secretary problem?. Statist. Sci. 4 (1989), 3, 282-289. DOI 10.1214/ss/1177012493 | MR 1015277
[6] Foss, S., Korshunov, D., Zachary, S.: An Introduction to Heavy-Tailed and Subexponential Distributions. Springer Science and Business Media, 2013. DOI 10.1007/978-1-4614-7101-1 | MR 3097424
[7] Horst, R., Tuy, H.: Global Optimization. Springer, 1996. DOI 10.1007/978-3-662-02947-3
[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. DOI 10.1007/1-84628-254-3
[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. MR 0378456
[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. DOI 10.1109/ijcnn.2005.1556452
[14] Peterka, V.: Bayesian system identification. In: Trends and Progress in System Identification (P. Eykhoff, ed.), Pergamon Press, Oxford 1981, pp. 239-304. DOI 10.1016/b978-0-08-025683-2.50013-2 | MR 0746139 | Zbl 0451.93059
[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. DOI 10.1109/jproc.2015.2494218
[16] Wolpert, D. H., Macready, W. G.: No free lunch theorems for optimization. IEEE Trans. Evolutionary Comput. 1 (1997), 1, 67-82. DOI 10.1109/4235.585893
[17] Zellner, A.: An Introduction to Bayesian Inference in Econometrics. J. Wiley, NY 1976. MR 1411451
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