  Classification models are very sensitive to data uncertainty, and finding
robust classifiers that are less sensitive to data uncertainty has raised great
interest in the machine learning literature. This paper aims to construct
robust \emph{Support Vector Machine} classifiers under feature data uncertainty
via two probabilistic arguments. The first classifier, \emph{Single
Perturbation}, reduces the local effect of data uncertainty with respect to one
given feature and acts as a local test that could confirm or refute the
presence of significant data uncertainty for that particular feature. The
second classifier, \emph{Extreme Empirical Loss}, aims to reduce the aggregate
effect of data uncertainty with respect to all features, which is possible via
a trade-off between the number of prediction model violations and the size of
these violations. Both methodologies are computationally efficient and our
extensive numerical investigation highlights the advantages and possible
limitations of the two robust classifiers on synthetic and real-life data.
