Detecting Outliers under Interval Uncertainty: A New Algorithm Based on Constraint Satisfaction

In many application areas, it is important to detect outliers. The traditional engineering approach to outlier detection is that we start with some “normal” values x1,...,xn, compute the sample average E, the sample standard deviation , and then mark a value x as an outlier if x is outside the k0-sigma interval [E k0 · ,E + k0 · ] (for some preselected parameter k0). In real life, we often have only interval ranges [x i ,xi] for the normal values x1,...,xn. In this case, we only have intervals of possible values for the bounds L def = E k0· and U def = E+k0· . We can therefore identify outliers as values that are outside all k0-sigma intervals, i.e., values which are outside the interval [L,U]. In general, the problem of computing L and U is NP-hard; a polynomialtime algorithm is known for the case when the measurements are suciently accurate, i.e., when “narrowed” intervals xi 1 + 2 n ·