Computationally Efficient Algorithms for High-Dimensional Robust Estimators

David M. Mount, Nathan S. Netanyahu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Given a set of n distinct points in d-dimensional space that are hypothesized to lie on a hyperplane, robust statistical estimators have been recently proposed for the parameters of the model that best fits these points. This paper presents efficient algorithms for computing median-based robust estimators (e.g., the Theil-Sen and repeated median (RM) estimators) in high-dimensional space. We briefly review basic computational geometry techniques that were used to achieve efficient algorithms in the 2-D case. Then generalization of these techniques to higher dimensions is introduced. Geometric observations are followed by a presentation of O(nd − 1 log n) expected time algorithms for the d-dimensional Theil-Sen and RM estimators. Both algorithms are space optimal; i.e., they require O(n) storage, for fixed d. Finally, an extension of the methodology to nonlinear domain(s) is demonstrated.
Original languageAmerican English
Title of host publicationFourth Canadian Conference on Computational Geometry
StatePublished - 1992

Bibliographical note

Place of conference:St. John's, New Foundland, Canada


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