Efficient NP tests for anomaly detection over birth-death type DTMCs

We propose computationally highly efficient Neyman-Pearson (NP) tests for anomaly detection over birth-death type discrete time Markov chains. Instead of relying on extensive Monte Carlo simulations (as in the case of the baseline NP), we directly approximate the log-likelihood density to match the desired false alarm rate; and therefore obtain our efficient implementations. The proposed algorithms are appropriate for processing large scale data in online applications with real time false alarm rate controllability. Since we do not require parameter tuning, our algorithms are also adaptive to non-stationarity in the data source. In our experiments, the proposed tests demonstrate superior detection power compared to the baseline NP while nearly achieving the desired rates with negligible computational resources.