Abnormality Detection with Rényi Divergence for Univariate Gaussian Data

This paper investigates the abnormality detection based on the Rényi divergence with the divergence order between 0 and 1. It is assumed that univariate Gaussian data samples are independent and identically distributed (i.i.d.). The distance between the estimated distribution from observed data and that from historical data under the normal condition is quantified by the Rényi divergence, the proposed test statistic. The false alarm rate (FAR) and the missed alarm rate (MAR) are derived analytically based on the distribution of the Rényi divergence. Under the abnormal condition, constant bias and multiplicative faults are considered. Taking both the FAR and MAR into consideration, the proposed detection algorithm can adaptively optimize the divergence order and threshold according to observed data. In the simulation, the analytical FAR and MAR results are verified by the Monte Carlo simulations, and the proposed algorithm is shown to outperform the Kullback-Leibler divergence based method.