Title: Stability Enhanced Large-Margin Classifier Selection,
Abstract: Stability is an important aspect of a classification procedure because
unstable predictions can potentially reduce users' trust in a classification
system and also harm the reproducibility of scientific conclusions. The major
goal of our work is to introduce a novel concept of classification instability,
i.e., decision boundary instability (DBI), and incorporate it with the
generalization error (GE) as a standard for selecting the most accurate and
stable classifier. Specifically, we implement a two-stage algorithm: (i)
initially select a subset of classifiers whose estimated GEs are not
significantly different from the minimal estimated GE among all the candidate
classifiers; (ii) the optimal classifier is chosen as the one achieving the
minimal DBI among the subset selected in stage (i). This general selection
principle applies to both linear and nonlinear classifiers. Large-margin
classifiers are used as a prototypical example to illustrate the above idea.
Our selection method is shown to be consistent in the sense that the optimal
classifier simultaneously achieves the minimal GE and the minimal DBI. Various
simulations and real examples further demonstrate the advantage of our method
over several alternative approaches.