Measuring intrusion detection capability: an information-theoretic approach

A fundamental problem in intrusion detection is what metric(s) can be used to objectively evaluate an intrusion detection system (IDS) in terms of its ability to correctly classify events as normal or intrusive. Traditional metrics (e.g., true positive rate and false positive rate) measure different aspects, but no single metric seems sufficient to measure the capability of intrusion detection systems. The lack of a single unified metric makes it difficult to fine-tune and evaluate an IDS. In this paper, we provide an in-depth analysis of existing metrics. Specifically, we analyze a typical cost-based scheme [6], and demonstrate that this approach is very confusing and ineffective when the cost factor is not carefully selected. In addition, we provide a novel information-theoretic analysis of IDS and propose a new metric that highly complements cost-based analysis. When examining the intrusion detection process from an information-theoretic point of view, intuitively, we should have less uncertainty about the input (event data) given the IDS output (alarm data). Thus, our new metric, C_{I D} (Intrusion Detection Capability), is defined as the ratio of the mutual information between the IDS input and output to the entropy of the input. C_{I D} has the desired property that: (1) It takes into account all the important aspects of detection capability naturally, i.e., true positive rate, false positive rate, positive predictive value, negative predictive value, and base rate; (2) it objectively provides an intrinsic measure of intrusion detection capability; and (3) it is sensitive to IDS operation parameters such as true positive rate and false positive rate, which can demonstrate the effect of the subtle changes of intrusion detection systems. We propose C_{I D} as an appropriate performance measure to maximize when fine-tuning an IDS. The obtained operation point is the best that can be achieved by the IDS in terms of its intrinsic ability to classify input data. We use numerical examples as well as experiments of actual IDSs on various data sets to show that by using C_{I D}, we can choose the best (optimal) operating point for an IDS and objectively compare different IDSs.