Stochastic Optimization for Numerical Evaluation of Imprecise Probabilities

Nicholas Syring, Ryan Martin
Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, PMLR 147:289-298, 2021.

Abstract

In applications of imprecise probability, analysts must compute lower (or upper) expectations, defined as the infimum of an expectation over a set of parameter values. Monte Carlo methods consistently approximate expectations at fixed parameter values, but can be costly to implement in grid search to locate minima over large subsets of the parameter space. We investigate the use of stochastic iterative root-finding methods for efficiently computing lower expectations. In two examples we illustrate the use of various stochastic approximation methods, and demonstrate their superior performance in comparison to grid search.

Cite this Paper

BibTeX
@InProceedings{pmlr-v147-syring21a, title = {Stochastic Optimization for Numerical Evaluation of Imprecise Probabilities}, author = {Syring, Nicholas and Martin, Ryan}, booktitle = {Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications}, pages = {289--298}, year = {2021}, editor = {Cano, Andrés and De Bock, Jasper and Miranda, Enrique and Moral, Serafı́n}, volume = {147}, series = {Proceedings of Machine Learning Research}, month = {06--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v147/syring21a/syring21a.pdf}, url = {https://proceedings.mlr.press/v147/syring21a.html}, abstract = {In applications of imprecise probability, analysts must compute lower (or upper) expectations, defined as the infimum of an expectation over a set of parameter values. Monte Carlo methods consistently approximate expectations at fixed parameter values, but can be costly to implement in grid search to locate minima over large subsets of the parameter space. We investigate the use of stochastic iterative root-finding methods for efficiently computing lower expectations. In two examples we illustrate the use of various stochastic approximation methods, and demonstrate their superior performance in comparison to grid search.} }
Endnote
%0 Conference Paper %T Stochastic Optimization for Numerical Evaluation of Imprecise Probabilities %A Nicholas Syring %A Ryan Martin %B Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2021 %E Andrés Cano %E Jasper De Bock %E Enrique Miranda %E Serafı́n Moral %F pmlr-v147-syring21a %I PMLR %P 289--298 %U https://proceedings.mlr.press/v147/syring21a.html %V 147 %X In applications of imprecise probability, analysts must compute lower (or upper) expectations, defined as the infimum of an expectation over a set of parameter values. Monte Carlo methods consistently approximate expectations at fixed parameter values, but can be costly to implement in grid search to locate minima over large subsets of the parameter space. We investigate the use of stochastic iterative root-finding methods for efficiently computing lower expectations. In two examples we illustrate the use of various stochastic approximation methods, and demonstrate their superior performance in comparison to grid search.
APA
Syring, N. & Martin, R.. (2021). Stochastic Optimization for Numerical Evaluation of Imprecise Probabilities. Proceedings of the Twelveth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 147:289-298 Available from https://proceedings.mlr.press/v147/syring21a.html.

Related Material