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Statistics > Machine Learning

arXiv:1302.7175 (stat)
[Submitted on 28 Feb 2013 (v1), last revised 1 Mar 2013 (this version, v2)]

Title:Estimating the Maximum Expected Value: An Analysis of (Nested) Cross Validation and the Maximum Sample Average

Authors:Hado van Hasselt
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Abstract:We investigate the accuracy of the two most common estimators for the maximum expected value of a general set of random variables: a generalization of the maximum sample average, and cross validation. No unbiased estimator exists and we show that it is non-trivial to select a good estimator without knowledge about the distributions of the random variables. We investigate and bound the bias and variance of the aforementioned estimators and prove consistency. The variance of cross validation can be significantly reduced, but not without risking a large bias. The bias and variance of different variants of cross validation are shown to be very problem-dependent, and a wrong choice can lead to very inaccurate estimates.
Subjects: Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Methodology (stat.ME)
Cite as: arXiv:1302.7175 [stat.ML]
  (or arXiv:1302.7175v2 [stat.ML] for this version)
  https://doi.org/10.48550/arXiv.1302.7175

Submission history

From: Hado van Hasselt [view email]
[v1] Thu, 28 Feb 2013 12:48:32 UTC (44 KB)
[v2] Fri, 1 Mar 2013 15:04:48 UTC (44 KB)
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