Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Stratied Finite Empirical Bernstein Sampling

Version 1 : Received: 17 January 2019 / Approved: 21 January 2019 / Online: 21 January 2019 (09:21:28 CET)
Version 2 : Received: 31 May 2019 / Approved: 31 May 2019 / Online: 31 May 2019 (10:37:48 CEST)

How to cite: Burgess, M.; Chapman, A. Stratied Finite Empirical Bernstein Sampling. Preprints 2019, 2019010202. Burgess, M.; Chapman, A. Stratied Finite Empirical Bernstein Sampling. Preprints 2019, 2019010202.


We derive a concentration inequality for the uncertainty in strati ed random sampling. Minimising this inequality leads to an iterated online method for choosing samples from the strata. The inequality is versatile and considers a range of factors including: the data ranges, weights, sizes of the strata, as well as the number of samples taken, the estimated sample variances and whether strata are sampled with or without replacement. We evaluate the improvement this method reliably offers against other methods over sets of synthetic data, and also in approximating the Shapley value of cooperative games. The method is seen to be competitive with the performance of perfect Neyman sampling, even without prior information on strata variances. We supply a multidimensional extension of our inequality and discuss some future applications.

Supplementary and Associated Material


Concentration Inequality, Empirical Bernstein Bound, Strati ed Random Sampling, Shapley Value Approximation


Computer Science and Mathematics, Probability and Statistics

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