Converting Output Scores from Outlier Detection Algorithms into Probability Estimates

Current outlier detection schemes typically output a numeric score representing the degree to which a given observation is an outlier. We argue that converting the scores into well-calibrated probability estimates is more favorable for several reasons. First, the probability estimates allow us to select the appropriate threshold for declaring outliers using a Bayesian risk model. Second, the probability estimates obtained from individual models can be aggregated to build an ensemble outlier detection framework. In this paper, we present two methods for transforming outlier scores into probabilities. The first approach assumes that the posterior probabilities follow a logistic sigmoid function and learns the parameters of the function from the distribution of outlier scores. The second approach models the score distributions as a mixture of exponential and Gaussian probability functions and calculates the posterior probabilites via the Bayes' rule. We evaluated the efficacy of both methods in the context of threshold selection and ensemble outlier detection. We also show that the calibration accuracy improves with the aid of some labeled examples.