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

Protecting Classifiers From Attacks. A Bayesian Approach