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There are substantial potential benefits to considering predictability when designing defenses against adaptive adversaries, including increasing the ability of defense systems to predict new attacker behavior and reducing the capacity of adversaries to anticipate defensive actions. This paper adopts such a perspective, leveraging the coevolutionary relationship between attackers and defenders to derive methods for predicting and countering attacks and for limiting the extent to which adversaries can learn about defense strategies. The proposed approach combines game theory with machine learning to model adversary adaptation in the learner's feature space, thereby producing classes of predictive and “moving target” defenses which are scientifically-grounded and applicable to problems of real-world scale and complexity. Case studies with large cyber security datasets demonstrate that the proposed algorithms outperform gold-standard techniques, offering effective and robust defense against evolving adversaries.