Bayesian stopping rule in discrete parameter space with multiple local maxima

Miroslav Kárný

Kybernetika (2019)

  • Volume: 55, Issue: 1, page 1-11
  • ISSN: 0023-5954

Abstract

top
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.

How to cite

top

Kárný, Miroslav. "Bayesian stopping rule in discrete parameter space with multiple local maxima." Kybernetika 55.1 (2019): 1-11. <http://eudml.org/doc/294489>.

@article{Kárný2019,
abstract = {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.},
author = {Kárný, Miroslav},
journal = {Kybernetika},
keywords = {global maximum; model structure; Bayesian estimation},
language = {eng},
number = {1},
pages = {1-11},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Bayesian stopping rule in discrete parameter space with multiple local maxima},
url = {http://eudml.org/doc/294489},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Kárný, Miroslav
TI - Bayesian stopping rule in discrete parameter space with multiple local maxima
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 1
SP - 1
EP - 11
AB - 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.
LA - eng
KW - global maximum; model structure; Bayesian estimation
UR - http://eudml.org/doc/294489
ER -

References

top
  1. Artin, E., The Gamma Function., Holt, Rinehart, Winston, NY 1964. MR0165148
  2. Barndorff-Nielsen, O., 10.1002/9781118857281, Wiley, NY 1978. Zbl1288.62007MR0489333DOI10.1002/9781118857281
  3. Berger, J. O., 10.1007/978-1-4757-4286-2, Springer, NY 1985. MR0804611DOI10.1007/978-1-4757-4286-2
  4. Bharti, K. K., Singh, P. K., 10.1016/j.eswa.2014.11.038, Expert Systems Appl. 42 (2015), 3105-3114. DOI10.1016/j.eswa.2014.11.038
  5. Ferguson, T. S., 10.1214/ss/1177012493, Statist. Sci. 4 (1989), 3, 282-289. MR1015277DOI10.1214/ss/1177012493
  6. Foss, S., Korshunov, D., Zachary, S., 10.1007/978-1-4614-7101-1, Springer Science and Business Media, 2013. MR3097424DOI10.1007/978-1-4614-7101-1
  7. Horst, R., Tuy, H., 10.1007/978-3-662-02947-3, Springer, 1996. DOI10.1007/978-3-662-02947-3
  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., 10.1007/1-84628-254-3, Springer, 2006. DOI10.1007/1-84628-254-3
  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. MR0378456
  12. Lizotte, D. J., Practical Bayesian Optimization., PhD Thesis, Edmonton, Alta 2008. 
  13. Novovičová, J., Malík, A., 10.1109/ijcnn.2005.1556452, In: Proc. of the IJCNN 2005, 16th International Joint Conference on Neural Networks, Montreal 2005, pp. 3272-3277. DOI10.1109/ijcnn.2005.1556452
  14. Peterka, V., 10.1016/b978-0-08-025683-2.50013-2, In: Trends and Progress in System Identification (P. Eykhoff, ed.), Pergamon Press, Oxford 1981, pp. 239-304. Zbl0451.93059MR0746139DOI10.1016/b978-0-08-025683-2.50013-2
  15. Shahriari, B., Swersky, K., Wang, Z., Adams, R. P., Freitas, N. de, 10.1109/jproc.2015.2494218, Proc. IEEE 104 (2016), 1, 148-175. DOI10.1109/jproc.2015.2494218
  16. Wolpert, D. H., Macready, W. G., 10.1109/4235.585893, IEEE Trans. Evolutionary Comput. 1 (1997), 1, 67-82. DOI10.1109/4235.585893
  17. Zellner, A., An Introduction to Bayesian Inference in Econometrics., J. Wiley, NY 1976. MR1411451

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.