  Machine Learning (ML) models are applied in a variety of tasks such as
network intrusion detection or Malware classification. Yet, these models are
vulnerable to a class of malicious inputs known as adversarial examples. These
are slightly perturbed inputs that are classified incorrectly by the ML model.
The mitigation of these adversarial inputs remains an open problem. As a step
towards understanding adversarial examples, we show that they are not drawn
from the same distribution than the original data, and can thus be detected
using statistical tests. Using thus knowledge, we introduce a complimentary
approach to identify specific inputs that are adversarial. Specifically, we
augment our ML model with an additional output, in which the model is trained
to classify all adversarial inputs. We evaluate our approach on multiple
adversarial example crafting methods (including the fast gradient sign and
saliency map methods) with several datasets. The statistical test flags sample
sets containing adversarial inputs confidently at sample sizes between 10 and
100 data points. Furthermore, our augmented model either detects adversarial
examples as outliers with high accuracy (> 80%) or increases the adversary's
cost - the perturbation added - by more than 150%. In this way, we show that
statistical properties of adversarial examples are essential to their
detection.
