Generative Bayesian Computation for Maximum Expected Utility

Generative Bayesian Computation (GBC) methods are developed to provide an efficient computational solution for maximum expected utility (MEU). We propose a density-free generative method based on quantiles that naturally calculates expected utility as a marginal of quantiles. Our approach uses a deep quantile neural estimator to directly estimate distributional utilities. Generative methods assume only the ability to simulate from the model and parameters and as such are likelihood-free. A large training dataset is generated from parameters and output together with a base distribution. Our method a number of computational advantages primarily being density-free with an efficient estimator of expected utility. A link with the dual theory of expected utility and risk taking is also discussed. To illustrate our methodology, we solve an optimal portfolio allocation problem with Bayesian learning and a power utility (a.k.a. fractional Kelly criterion). Finally, we conclude with directions for future research.

Protecting Classifiers From Attacks. A Bayesian Approach

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.

Adversarial classification: An adversarial risk analysis approach

Classification problems in security settings are usually contemplated as confrontations in which one or more adversaries try to fool a classifier to obtain a benefit. Most approaches to such adversarial classification problems have focused on game theoretical ideas with strong underlying common knowledge assumptions, which are actually not realistic in security domains. We provide an alternative framework to such problem based on adversarial risk analysis, which we illustrate with several examples. Computational and implementation issues are discussed.