Robust regression and outlier detection
Robust regression and outlier detection
The feasible solution algorithm for least trimmed squares regression
Computational Statistics & Data Analysis
Applications of semidefinite programming
HPOPT '96 Proceedings of the Stieltjes workshop on High performance optimization techniques
Improved feasible solution algorithms for high breakdown estimation
Computational Statistics & Data Analysis
New algorithms for computing the least trimmed squares regression estimator
Computational Statistics & Data Analysis
Finite Exact Branch-and-Bound Algorithms for Concave Minimization over Polytopes
Journal of Global Optimization
A polyhedral study of nonconvex quadratic programs with box constraints
Mathematical Programming: Series A and B
A branch-and-cut algorithm for nonconvex quadratic programs with box constraints
Mathematical Programming: Series A and B
Computing LTS Regression for Large Data Sets
Data Mining and Knowledge Discovery
A Numerical Approach for Solving Some Convex Maximization Problems
Journal of Global Optimization
Classification and Regression via Integer Optimization
Operations Research
RelaxMCD: Smooth optimisation for the Minimum Covariance Determinant estimator
Computational Statistics & Data Analysis
A relaxed approach to combinatorial problems in robustness and diagnostics
Statistics and Computing
Editorial: Special issue on variable selection and robust procedures
Computational Statistics & Data Analysis
Outlier detection and robust covariance estimation using mathematical programming
Advances in Data Analysis and Classification
Robust fuzzy regression analysis
Information Sciences: an International Journal
An Adversarial Optimization Approach to Efficient Outlier Removal
Journal of Mathematical Imaging and Vision
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Robust linear regression is one of the most popular problems in the robust statistics community. It is often conducted via least trimmed squares, which minimizes the sum of the k smallest squared residuals. Least trimmed squares has desirable properties and forms the basis on which several recent robust methods are built, but is very computationally expensive due to its combinatorial nature. It is proven that the least trimmed squares problem is equivalent to a concave minimization problem under a simple linear constraint set. The ''maximum trimmed squares'', an ''almost complementary'' problem which maximizes the sum of the q smallest squared residuals, in direct pursuit of the set of outliers rather than the set of clean points, is introduced. Maximum trimmed squares (MTS) can be formulated as a semi-definite programming problem, which can be solved efficiently in polynomial time using interior point methods. In addition, under reasonable assumptions, the maximum trimmed squares problem is guaranteed to identify outliers, no mater how extreme they are.