Excess Optimism, or: What is the Prediction Error of an Estimator Tuned by SURE?

Dec 13 (Tuesday) at Noon GHC-8102

Speaker: Ryan Tibshirani

Abstract: Nearly all estimators in statistical prediction come with an associated tuning parameter, in one way or another. Common practice, given data, is to choose the tuning parameter value that minimizes a constructed estimate of the prediction error of the estimator. Of course, estimating prediction error has a long history in statistics, and many methods have been proposed for this problem; we focus on Stein’s unbiased risk estimator, or SURE (Stein, 1981; Efron, 1986), which forms an unbiased estimate of the prediction error by augmenting the observed training error with an estimate of the degrees of freedom of our estimator. Parameter tuning via SURE minimization has been advocated by many authors, in a wide variety of problem settings. In general, it is natural to ask: what is the prediction error of the SURE-tuned estimator? The most obvious estimate for this quantity is the value of the SURE criterion at its minimum. However, this is no longer itself unbiased; in fact, we would expect the minimum of SURE to be systematically biased downwards as an estimate of the prediction error of the SURE-tuned estimator. We formally describe and study this bias. This is based on work that is in progress, with Saharon Rosset.