Computation of Least Trimmed Squares: A Branch-and-Bound framework with Hyperplane Arrangement Enhancements
We study computational aspects of a key problem in robust statistics -- the penalized least trimmed squares (LTS) regression problem, a robust estimator that mitigates the influence of outliers in data by capping residuals with large magnitudes. Although statistically attractive, penalized LTS is NP-hard, and existing mixed-integer optimization (MIO) formulations scale poorly due to weak relaxations and exponential worst-case complexity in the number of observations. We propose a new MIO formulation that embeds hyperplane arrangement logic into a perspective reformulation, explicitly enforcing structural properties of optimal solutions. We show that, if the number of features is fixed, th...
| Authors | Xiang Meng, Andrés Gómez, Rahul Mazumder |
|---|---|
| Primary category | math.OC |
| Published | 13 April 2026 |
| Last updated at source | 14 April 2026 |
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