Statistical foundations of audit trail analysis for the detection of computer misuse

We model computer transactions as generated by two stationary stochastic processes, the legitimate (normal) process N and the misuse process M. We define misuse (anomaly) detection to be the identification of transactions most likely to have been generated by M. We formally demonstrate that the accuracy of misuse detectors is bounded by a function of the difference of the densities of the processes N and M over the space of transactions. In practice, detection accuracy can be far below this bound, and generally improves with increasing sample size of historical (training) data. Careful selection of transaction attributes also can improve detection accuracy; we suggest several criteria for attribute selection, including adequate sampling rate and separation between models. We demonstrate that exactly optimizing even the simplest of these criteria is NP-hard, thus motivating a heuristic approach. We further differentiate between modeling (density estimation) and nonmodeling approaches