Adaptive Sampling for Estimating Distributions: A Bayesian Upper Confidence Bound Approach

Dhruva Kartik, Neeraj Sood, Urbashi Mitra, Tara Javidi
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:1169-1179, 2021.

Abstract

The problem of adaptive sampling for estimating probability mass functions (pmf) uniformly well is considered. Performance of the sampling strategy is measured in terms of the worst-case mean squared error. A Bayesian variant of the existing upper confidence bound (UCB) based approaches is proposed. It is shown analytically that the performance of this Bayesian variant is no worse than the existing approaches. The posterior distribution on the pmfs in the Bayesian setting allows for a tighter computation of upper confidence bounds which leads to significant performance gains in practice. Using this approach, adaptive sampling protocols are proposed for estimating SARS-CoV-2 seroprevalence in various groups such as location and ethnicity. The effectiveness of this strategy is discussed using data obtained from a seroprevalence survey in Los Angeles county.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-kartik21a, title = {Adaptive Sampling for Estimating Distributions: A Bayesian Upper Confidence Bound Approach}, author = {Kartik, Dhruva and Sood, Neeraj and Mitra, Urbashi and Javidi, Tara}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {1169--1179}, year = {2021}, editor = {Jadbabaie, Ali and Lygeros, John and Pappas, George J. and A. Parrilo, Pablo and Recht, Benjamin and Tomlin, Claire J. and Zeilinger, Melanie N.}, volume = {144}, series = {Proceedings of Machine Learning Research}, month = {07 -- 08 June}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v144/kartik21a/kartik21a.pdf}, url = {https://proceedings.mlr.press/v144/kartik21a.html}, abstract = {The problem of adaptive sampling for estimating probability mass functions (pmf) uniformly well is considered. Performance of the sampling strategy is measured in terms of the worst-case mean squared error. A Bayesian variant of the existing upper confidence bound (UCB) based approaches is proposed. It is shown analytically that the performance of this Bayesian variant is no worse than the existing approaches. The posterior distribution on the pmfs in the Bayesian setting allows for a tighter computation of upper confidence bounds which leads to significant performance gains in practice. Using this approach, adaptive sampling protocols are proposed for estimating SARS-CoV-2 seroprevalence in various groups such as location and ethnicity. The effectiveness of this strategy is discussed using data obtained from a seroprevalence survey in Los Angeles county.} }
Endnote
%0 Conference Paper %T Adaptive Sampling for Estimating Distributions: A Bayesian Upper Confidence Bound Approach %A Dhruva Kartik %A Neeraj Sood %A Urbashi Mitra %A Tara Javidi %B Proceedings of the 3rd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2021 %E Ali Jadbabaie %E John Lygeros %E George J. Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire J. Tomlin %E Melanie N. Zeilinger %F pmlr-v144-kartik21a %I PMLR %P 1169--1179 %U https://proceedings.mlr.press/v144/kartik21a.html %V 144 %X The problem of adaptive sampling for estimating probability mass functions (pmf) uniformly well is considered. Performance of the sampling strategy is measured in terms of the worst-case mean squared error. A Bayesian variant of the existing upper confidence bound (UCB) based approaches is proposed. It is shown analytically that the performance of this Bayesian variant is no worse than the existing approaches. The posterior distribution on the pmfs in the Bayesian setting allows for a tighter computation of upper confidence bounds which leads to significant performance gains in practice. Using this approach, adaptive sampling protocols are proposed for estimating SARS-CoV-2 seroprevalence in various groups such as location and ethnicity. The effectiveness of this strategy is discussed using data obtained from a seroprevalence survey in Los Angeles county.
APA
Kartik, D., Sood, N., Mitra, U. & Javidi, T.. (2021). Adaptive Sampling for Estimating Distributions: A Bayesian Upper Confidence Bound Approach. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:1169-1179 Available from https://proceedings.mlr.press/v144/kartik21a.html.

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