We introduce a new anomaly detection methodology for data with latent dependency structure. As a particular instantiation, we derive a hidden Markov anomaly detector that extends the regular one-class support vector machine. We optimize the approach, which is non-convex, via a DC (difference of convex functions) algorithm, and show that the parameter v can be conveniently used to control the number of outliers in the model. The empirical evaluation on artificial and real data from the domains of computational biology and computational sustainability shows that the approach can achieve significantly higher anomaly detection performance than the regular one-class SVM.