Outlier Detection Under Interval Uncertainty: Algorithmic Solvability and Computational Complexity

In many application areas, it is important to detect outliers. Traditional engineering approach to outlier detection is that we start with some "normal" values x1 ; : : : ; xn , compute the sample average E, the sample standard variation oe, and then mark a value x as an outlier if x is outside the k0-sigma interval [E \Gamma k0 \Delta oe; E+k0 \Delta oe] (for some pre-selected parameter k0 ). In real life, we often have only interval ranges [x i ; x i ] for the normal values x1 ; : : : ; xn . In this case, we only have intervals of possible values for the bounds E \Gamma k0 \Delta oe and E+k0 \Delta oe. We can therefore identify outliers as values that are outside all k0-sigma intervals