  We consider the sequential anomaly detection problem in the one-class setting
when only the anomalous sequences are available and propose an adversarial
sequential detector by solving a minimax problem to find an optimal detector
against the worst-case sequences from a generator. The generator captures the
dependence in sequential events using the marked point process model. The
detector sequentially evaluates the likelihood of a test sequence and compares
it with a time-varying threshold, also learned from data through the minimax
problem. We demonstrate our proposed method's good performance using numerical
experiments on simulations and proprietary large-scale credit card fraud
datasets. The proposed method can generally apply to detecting anomalous
sequences.
