Fast and Exact Least Absolute Deviations Line Fitting via Piecewise Affine Lower-Bounding
Published:Dec 25, 2025 05:00
•1 min read
•ArXiv Stats ML
Analysis
This paper introduces a novel algorithm, Piecewise Affine Lower-Bounding (PALB), for solving the Least Absolute Deviations (LAD) line fitting problem. LAD is robust to outliers but computationally expensive compared to least squares. The authors address the lack of readily available and efficient implementations of existing LAD algorithms by presenting PALB. The algorithm's correctness is proven, and its performance is empirically validated on synthetic and real-world datasets, demonstrating log-linear scaling and superior speed compared to LP-based and IRLS-based solvers. The availability of a Rust implementation with a Python API enhances the practical value of this research, making it accessible to a wider audience. This work contributes significantly to the field by providing a fast, exact, and readily usable solution for LAD line fitting.
Key Takeaways
Reference
“PALB exhibits empirical log-linear scaling.”