Numerical Methods for Computing Plausibility and Belief Distributions of Consequences of a Subjective Model of Object of Research
Numerical methods for computing plausibility and belief distributions of consequences of a subjective model are considered. More precisely, related constrained optimization problems are studied. Error estimates of the proposed algorithms are obtained. Techniques for taking into account the information about the consequence available to the researcher for improving the accuracy of computations are discussed.
Keywordsconstrained optimization global optimization subjective modeling plausibility belief
Unable to display preview. Download preview PDF.
- 2.N. N. Kalitkin, Numerical Methods, Ed. by A. A. Samarskii, 2nd ed. (BKhV, St. Peterburg, 2011) [in Russian].Google Scholar
- 7.J. M. Hernandez-Lobato, M. A. Gelbart, M. W. Hoffman, R. P. Adams, and Z. Ghahramani, “Predictive entropy search for bayesian optimization with unknown constraints,” in Proc. 32nd Int. Conf. on Machine Learning, Lille, France, 2015, Vol. 37 of JMLR: W&CP. arXiv:1502.05312 stat.MLGoogle Scholar
- 8.V. Picheny, “A stepwise uncertainty reduction approach to constrained global optimization,” in Proc. 17th Int. Conf. on Artificial Intelligence and Statistics, Vol. 33 of JMLR: W&CP, 2014.Google Scholar
- 9.J. R. Gardner, M. J. Kusner, Z. Xu, K. Q. Weinberger, J. P. Cunningham, “Bayesian optimization with inequality constraints,” in Proc. 31st Int. Conf. on Machine Learning, Beijing, 2014, Vol. 32 of JMLR: W&CP.Google Scholar
- 11.V. Picheny, R. B. Gramacy, S. M. Wild, and S. Le Dirigabel, “Bayesian optimization under mixed constraints with a slack-variable augmented Lagrangian.” arXiv:1605.09466 [stat.CO]. Cited October, 2016.Google Scholar
- 12.F. P. Vasil’ev, Optimization Methods (Faktorial, Moscow, 2002) [in Russian].Google Scholar