Robust regression and outlier detection
Robust regression and outlier detection
Robust regression methods for computer vision: a review
International Journal of Computer Vision
Lower bounds for algebraic computation trees with integer inputs
SIAM Journal on Computing
On the complexity of approximating extremal determinants in matrices
Journal of Complexity
A General Approach to Removing Degeneracies
SIAM Journal on Computing
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
An approximation algorithm for least median of squares regression
Information Processing Letters
New Lower Bounds for Convex Hull Problems in Odd Dimensions
SIAM Journal on Computing
A practical approximation algorithm for the LMS line estimator
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Data structures for mobile data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Low-Dimensional Linear Programming with Violations
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Proceedings of the nineteenth annual symposium on Computational geometry
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
A practical approximation algorithm for the LMS line estimator
Computational Statistics & Data Analysis
NBS: A new representation for point surfaces based on genetic clustering algorithm
Computers and Graphics
Computing the least median of squares estimator in time O(nd)
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
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We consider the exact and approximate computational complexity of the multivariate LMS linear regression estimator. The LMS estimator is among the most widely used robust linear statistical estimators. Given a set of n points in ℝd and a parameter k, the problem is equivalent to computing the narrowest slab bounded by two parallel hyperplanes that contains k of the points. We present algorithms for the exact and approximate versions of the multivariate LMS problem. We also provide nearly matching lowerbounds for these problems, under the assumption that deciding whether n given points in ℝd are affinely nondegenerate requires Ω(nd) time.