  Cross-validation is the de facto standard for predictive model evaluation and
selection. In proper use, it provides an unbiased estimate of a model's
predictive performance. However, data sets often undergo various forms of
data-dependent preprocessing, such as mean-centering, rescaling, dimensionality
reduction, and outlier removal. It is often believed that such preprocessing
stages, if done in an unsupervised manner (that does not incorporate the class
labels or response values) are generally safe to do prior to cross-validation.
  In this paper, we study three commonly-practiced preprocessing procedures
prior to a regression analysis: (i) variance-based feature selection; (ii)
grouping of rare categorical features; and (iii) feature rescaling. We
demonstrate that unsupervised preprocessing can, in fact, introduce a
substantial bias into cross-validation estimates and potentially hurt model
selection. This bias may be either positive or negative and its exact magnitude
depends on all the parameters of the problem in an intricate manner. Further
research is needed to understand the real-world impact of this bias across
different application domains, particularly when dealing with small sample
sizes and high-dimensional data.
