arXiv subjects

Stefan Volz

Publications and source records attributed to Stefan Volz.

2 recordsLinked to original sources

arXiv2025

Fast and Exact Least Absolute Deviations Line Fitting via Piecewise Affine Lower-Bounding

Least-absolute-deviations (LAD) line fitting is robust to outliers but computationally more involved than least squares regression. Although the literature includes linear and near-linear time algorithms for the LAD line fitting problem, these methods are difficult to implement and, to our knowledge, lack maintained public implementations. As a result, practitioners often resort to linear programming (LP) based methods such as the simplex-based Barrodale-Roberts method and interior-point methods, or on iteratively reweighted least squares (IRLS) approximation which does not guarantee exact solutions. To close this gap, we propose the Piecewise Affine Lower-Bounding (PALB) method, an exact algorithm for LAD line fitting. PALB uses supporting lines derived from subgradients to build piecewise-affine lower bounds, and employs a subdivision scheme involving minima of these lower bounds. We prove correctness and provide bounds on the number of iterations. On synthetic datasets with varied signal types and noise including heavy-tailed outliers as well as a real dataset from the NOAA's Integrated Surface Database, PALB exhibits empirical log-linear scaling. It is consistently faster than publicly available implementations of LP based and IRLS based solvers. We provide a reference implementation written in Rust with a Python API.

stat.ML↗

arXiv2025

Degrees-of-freedom penalized piecewise regression

Many popular piecewise regression models rely on minimizing a cost function on the model fit with a linear penalty on the number of segments. However, this penalty does not take into account varying complexities of the model functions on the segments potentially leading to overfitting when models with varying complexities, such as polynomials of different degrees, are used. In this work, we enhance on this approach by instead using a penalty on the sum of the degrees of freedom over all segments, called degrees-of-freedom penalized piecewise regression (DofPPR). We show that the solutions of the resulting minimization problem are unique for almost all input data in a least squares setting. We develop a fast algorithm which does not only compute a minimizer but also determines an optimal hyperparameter -- in the sense of rolling cross validation with the one standard error rule -- exactly. This eliminates manual hyperparameter selection. Our method supports optional user parameters for incorporating domain knowledge. We provide an open-source Python/Rust code for the piecewise polynomial least squares case which can be extended to further models. We demonstrate the practical utility through a simulation study and by applications to real data. A constrained variant of the proposed method gives state-of-the-art results in the Turing benchmark for unsupervised changepoint detection.

stat.ME↗