Previous |  Up |  Next

Article

Title: Bayesian stopping rule in discrete parameter space with multiple local maxima (English)
Author: Kárný, Miroslav
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 55
Issue: 1
Year: 2019
Pages: 1-11
Summary lang: English
.
Category: math
.
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. (English)
Keyword: global maximum
Keyword: model structure
Keyword: Bayesian estimation
MSC: 62L15
MSC: 62P99
idZBL: Zbl 07088875
idMR: MR3935411
DOI: 10.14736/kyb-2019-1-0001
.
Date available: 2019-05-07T11:01:25Z
Last updated: 2020-02-27
Stable URL: http://hdl.handle.net/10338.dmlcz/147700
.
Reference: [1] Artin, E.: The Gamma Function..Holt, Rinehart, Winston, NY 1964. MR 0165148
Reference: [2] Barndorff-Nielsen, O.: Information and Exponential Families in Statistical Theory..Wiley, NY 1978. Zbl 1288.62007, MR 0489333, 10.1002/9781118857281
Reference: [3] Berger, J. O.: Statistical Decision Theory and Bayesian Analysis..Springer, NY 1985. MR 0804611, 10.1007/978-1-4757-4286-2
Reference: [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. 10.1016/j.eswa.2014.11.038
Reference: [5] Ferguson, T. S.: Who solved the secretary problem?.Statist. Sci. 4 (1989), 3, 282-289. MR 1015277, 10.1214/ss/1177012493
Reference: [6] Foss, S., Korshunov, D., Zachary, S.: An Introduction to Heavy-Tailed and Subexponential Distributions..Springer Science and Business Media, 2013. MR 3097424, 10.1007/978-1-4614-7101-1
Reference: [7] Horst, R., Tuy, H.: Global Optimization..Springer, 1996. 10.1007/978-3-662-02947-3
Reference: [8] Kárný, M.: Algorithms for determining the model structure of a controlled system..Kybernetika 9 (1983), 2, 164-178.
Reference: [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. 10.1007/1-84628-254-3
Reference: [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.
Reference: [11] Knuth, D. E.: The Art of Computer Programming, Sorting and Searching..Addison-Wesley, Reading 1973. MR 0378456
Reference: [12] Lizotte, D. J.: Practical Bayesian Optimization..PhD Thesis, Edmonton, Alta 2008.
Reference: [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. 10.1109/ijcnn.2005.1556452
Reference: [14] Peterka, V.: Bayesian system identification..In: Trends and Progress in System Identification (P. Eykhoff, ed.), Pergamon Press, Oxford 1981, pp. 239-304. Zbl 0451.93059, MR 0746139, 10.1016/b978-0-08-025683-2.50013-2
Reference: [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. 10.1109/jproc.2015.2494218
Reference: [16] Wolpert, D. H., Macready, W. G.: No free lunch theorems for optimization..IEEE Trans. Evolutionary Comput. 1 (1997), 1, 67-82. 10.1109/4235.585893
Reference: [17] Zellner, A.: An Introduction to Bayesian Inference in Econometrics..J. Wiley, NY 1976. MR 1411451
.

Files

Files Size Format View
Kybernetika_55-2019-1_1.pdf 568.0Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo