Outlier Detection under Interval Uncertainty: Algorithmic Solvability and Computational Complexity

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Luc Longpre, The University of Texas at El PasoFollow
Praveen Patangay
Scott Ferson
Lev Ginzburg

Publication Date

7-2004

Comments

Technical Report: UTEP-CS-03-10f

Short version published in: Ivan Lirkov, Svetozar Margenov, Jerzy Wasniewski, and Plamen Yalamov (eds.), Large-Scale Scientific Computing, Proceedings of the 4th International Conference LSSC'2003, Sozopol, Bulgaria, June 4-8, 2003, Springer Lecture Notes in Computer Science, 2004, Vol. 2907, pp. 276-283; full paper published in Reliable Computing, 2005, Vol. 11, No. 1, pp. 59-76.

Abstract

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 sigma, and then mark a value x as an outlier if x is outside the k0-sigma interval [E-k0*sigma,E+k0*sigma] (for some pre-selected parameter k0). In real life, we often have only interval ranges [xi] for the normal values x1,...,xn. In this case, we only have intervals of possible values for the bounds E-k0*sigma and E+k0*sigma. We can therefore identify outliers as values that are outside all k0-sigma intervals. In this paper, we analyze the computational complexity of these outlier detection problems, and provide efficient algorithms that solve some of these problems (under reasonable conditions).