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Research in NLP is often supported by experimental results, and improvedreporting of such results can lead to better understanding and morereproducible science. In this paper we analyze three statistical estimators forexpected validation performance, a tool used for reporting performance (e.g.,accuracy) as a function of computational budget (e.g., number of hyperparametertuning experiments). Where previous work analyzing such estimators focused onthe bias, we also examine the variance and mean squared error (MSE). In bothsynthetic and realistic scenarios, we evaluate three estimators and find theunbiased estimator has the highest variance, and the estimator with thesmallest variance has the largest bias; the estimator with the smallest MSEstrikes a balance between bias and variance, displaying a classic bias-variancetradeoff. We use expected validation performance to compare between differentmodels, and analyze how frequently each estimator leads to drawing incorrectconclusions about which of two models performs best. We find that the twobiased estimators lead to the fewest incorrect conclusions, which hints at theimportance of minimizing variance and MSE.

Expected Validation Performance and Estimation of a Random Variable's Maximum