Using Supervised Learning to Improve Monte Carlo Integral Estimation
By Brendan D. Tracey, David Hilton Wolpert, Juan José Palacios Alonso. 2011
27 citations recorded by the source corpus.
Monte Carlo techniques are used to estimate the integrals of a function using randomly generated samples. The interest in uncertainty quantification and robust design makes calculating the expected values of such functions (e.g., performance measures) important. Recent developments in scramjets, aircraft technology forecasting, structural reliability, and robust low-boom aircraft designs use Monte Carlo techniques to ensure the appropriate quantification of uncertainties. Because of high variance and slow convergence, Monte Carlo techniques require a large number of function evaluations, limiting the fidelity of the tools that can be used to predict performance. Stacked Monte Carlo is presented, which is a new method for postprocessing an existing set of Monte Carlo samples to improve integral estimation. Stacked Monte Carlo is based on combining fitting functions with cross-validation and should reduce the variance of any type of Monte Carlo integral estimate (importance sampling, quasi-Monte Carlo, etc....
Subfields: Aerospace Engineering, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Aerospace Engineering
- Karen E. Willcox
- Max D. Gunzburger
- Nicolas Chopin
- Benjamin Peherstorfer
- Chris J. Oates
- Mark A. Girolami
In Statistics and Probability
- Chris J. Oates
- Benjamin Peherstorfer
- Max D. Gunzburger
- Mark A. Girolami
- Karen E. Willcox
- Nicolas Chopin
- Qiang Liu
- Paris Perdikaris
Citations in the corpus
- Control functionals for Monte Carlo integration (2014, background): “ng point is establish a trade-o between random sampling and deterministic approximation, as suggested on several separate occasions by authors including Heinrich (1995); Speight (2009); Giles (2013); Tracey et al. (2013); Graham et al. (2015). Consider a dichotomy of available states D= fx ign i=1 i”
- Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, methodology): “The StackMC method presented in [203] successively constructs machine-learning-based low-fidelity models and combines them with the control variate framework.”
- Control Functionals for Quasi-Monte Carlo Integration (2015, methodology): “duction for QMC rules, building on kernel methods and recent work in the Monte Carlo setting due to [22, 31].”
- Optimal Model Management for Multifidelity Monte Carlo Estimation (2016, methodology): “StackedMC [47] uses the control variate method and data-fit surrogate models.”