Sequential Detection of Anomalies in Noisy Outputs of an Unknown Function Using Gaussian and Yule-Simon Processes

Detection of anomalies is a common and important problem, especially when anomalies are rare and labels are difficult to acquire. Here we sequentially detect outliers in the outputs of an unknown function, which have been distorted by noise. We model the sequence of outputs by using Yule-Simon processes and provide an iterative algorithm for learning the function from input and output data using Gaussian processes. We tested our method by using both synthetic and real-world data. The experimental results indicate excellent performance of the proposed method.