Adversarial Learning with Bayesian Hierarchical Mixtures of Experts

Many data mining applications operate in adversarial environment, for example, webpage ranking in the presence of web spam. A growing number of adversarial data mining techniques are recently developed, providing robust solutions under specific defense-attack models. Existing techniques are tied to distributional assumptions geared towards minimizing the undesirable impact of given attack models. However, the large variety of attack strategies renders the adversarial learning problem multimodal. Therefore, it calls for a more flexible modeling ideology for equivocal input. In this paper we present a Bayesian hierarchical mixtures of experts for adversarial learning. The technique groups data into soft partitions and fits simple function approximators, referred to as “experts”, within each. Experts are ranked using gating functions for each input. Ambiguous input is predicted competitively by multiple experts, while unambiguous input is effectively predicted by a single expert. Optimal attacks minimizing the likelihood of malicious data are modeled interactively at both expert and gating levels in the learning hierarchy. We demonstrate that our adversarial hierarchicalmixtures-of-experts learning model is robust against adversarial attacks on both artificial and real data.