  Classification problems in security settings are usually modeled as
confrontations in which an adversary tries to fool a classifier manipulating
the covariates of instances to obtain a benefit. Most approaches to such
problems have focused on game-theoretic ideas with strong underlying common
knowledge assumptions, which are not realistic in the security realm. We
provide an alternative Bayesian framework that accounts for the lack of precise
knowledge about the attacker's behavior using adversarial risk analysis. A key
ingredient required by our framework is the ability to sample from the
distribution of originating instances given the possibly attacked observed one.
We propose a sampling procedure based on approximate Bayesian computation, in
which we simulate the attacker's problem taking into account our uncertainty
about his elements. For large scale problems, we propose an alternative,
scalable approach that could be used when dealing with differentiable
classifiers. Within it, we move the computational load to the training phase,
simulating attacks from an adversary, adapting the framework to obtain a
classifier robustified against attacks.
