Output-weighted optimal sampling for Bayesian regression and rare event statistics using few samples
| Autor: | Themistoklis P. Sapsis |
|---|---|
| Přispěvatelé: | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Machine Learning Multivariate random variable Computer science Active learning (machine learning) General Mathematics General Physics and Astronomy Machine Learning (stat.ML) Statistics - Applications Statistics - Computation 01 natural sciences Machine Learning (cs.LG) 010305 fluids & plasmas Statistics - Machine Learning 0103 physical sciences Statistics Applications (stat.AP) 0101 mathematics Computation (stat.CO) Event (probability theory) Optimal sampling General Engineering Function (mathematics) 010101 applied mathematics Bayesian linear regression Research Article |
| Zdroj: | Proc Math Phys Eng Sci arXiv |
| Popis: | For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify its statistics, using the minimum number of function evaluations. This problem can been seen in the context of active learning or optimal experimental design. We employ Bayesian regression to represent the derived model uncertainty due to finite and small number of input-output pairs. In this context we evaluate existing methods for optimal sample selection, such as model error minimization and mutual information maximization. We show that for the case of known output variance, the commonly employed criteria in the literature do not take into account the output values of the existing input-output pairs, while for the case of unknown output variance this dependence can be very weak. We introduce a criterion that takes into account the values of the output for the existing samples and adaptively selects inputs from regions of the parameter space which have important contribution to the output. The new method allows for application to high-dimensional inputs, paving the way for optimal experimental design in high-dimensions. 34 pages; 13 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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