A Framework for Sample Efficient Interval Estimation with Control Variates

Shengjia Zhao, Christopher Yeh, Stefano Ermon
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:4583-4592, 2020.

Abstract

We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this problem in the general case, improved performance is possible under additional assumptions. In particular, we design an estimation algorithm to take advantage of side information in the form of a control variate, leveraging order statistics. Under certain conditions on the quality of the control variates, we show improved asymptotic efficiency compared to existing estimation algorithms. Empirically, we demonstrate superior performance on several real world surveying and estimation tasks where we use regression models as control variates.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-zhao20e, title = {A Framework for Sample Efficient Interval Estimation with Control Variates}, author = {Zhao, Shengjia and Yeh, Christopher and Ermon, Stefano}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {4583--4592}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/zhao20e/zhao20e.pdf}, url = {https://proceedings.mlr.press/v108/zhao20e.html}, abstract = {We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this problem in the general case, improved performance is possible under additional assumptions. In particular, we design an estimation algorithm to take advantage of side information in the form of a control variate, leveraging order statistics. Under certain conditions on the quality of the control variates, we show improved asymptotic efficiency compared to existing estimation algorithms. Empirically, we demonstrate superior performance on several real world surveying and estimation tasks where we use regression models as control variates.} }
Endnote
%0 Conference Paper %T A Framework for Sample Efficient Interval Estimation with Control Variates %A Shengjia Zhao %A Christopher Yeh %A Stefano Ermon %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-zhao20e %I PMLR %P 4583--4592 %U https://proceedings.mlr.press/v108/zhao20e.html %V 108 %X We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this problem in the general case, improved performance is possible under additional assumptions. In particular, we design an estimation algorithm to take advantage of side information in the form of a control variate, leveraging order statistics. Under certain conditions on the quality of the control variates, we show improved asymptotic efficiency compared to existing estimation algorithms. Empirically, we demonstrate superior performance on several real world surveying and estimation tasks where we use regression models as control variates.
APA
Zhao, S., Yeh, C. & Ermon, S.. (2020). A Framework for Sample Efficient Interval Estimation with Control Variates. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:4583-4592 Available from https://proceedings.mlr.press/v108/zhao20e.html.

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