  Machine Learning models have been shown to be vulnerable to adversarial
examples, ie. the manipulation of data by a attacker to defeat a defender's
classifier at test time. We present a novel probabilistic definition of
adversarial examples in perfect or limited knowledge setting using prior
probability distributions on the defender's classifier. Using the asymptotic
properties of the logistic regression, we derive a closed-form expression of
the intensity of any adversarial perturbation, in order to achieve a given
expected misclassification rate. This technique is relevant in a threat model
of known model specifications and unknown training data. To our knowledge, this
is the first method that allows an attacker to directly choose the probability
of attack success. We evaluate our approach on two real-world datasets.
