  Research in NLP is often supported by experimental results, and improved
reporting of such results can lead to better understanding and more
reproducible science. In this paper we analyze three statistical estimators for
expected validation performance, a tool used for reporting performance (e.g.,
accuracy) as a function of computational budget (e.g., number of hyperparameter
tuning experiments). Where previous work analyzing such estimators focused on
the bias, we also examine the variance and mean squared error (MSE). In both
synthetic and realistic scenarios, we evaluate three estimators and find the
unbiased estimator has the highest variance, and the estimator with the
smallest variance has the largest bias; the estimator with the smallest MSE
strikes a balance between bias and variance, displaying a classic bias-variance
tradeoff. We use expected validation performance to compare between different
models, and analyze how frequently each estimator leads to drawing incorrect
conclusions about which of two models performs best. We find that the two
biased estimators lead to the fewest incorrect conclusions, which hints at the
importance of minimizing variance and MSE.
