A model-based bayesian approach to anomaly detection via mixture models

Abstract

In this work, we present a Bayesian model-based approach to anomaly detection using mixture models. Our proposed method, called the filtering model, only requires us to specify a parametric model, that depends on an unknown θ, to describe the behavior of the typical data and uses the chosen model to determine the underlying distribution of the component of the mixture responsible for capturing anomalies. The method is able to simultaneously estimate the classification for each observation and θ, while taking the estimate of θ to be a convex combination of each possible estimate generated by a subsample. For this reason, it can also be used for robust parameter estimation. We consider estimation using Markov chain Monte Carlo techniques, and in particular the Metropolis-Hastings algorithm, and present applications for chemical, health and demographic data.