TY - JOUR A1 - Volz, Stefan A1 - Storath, Martin A1 - Weinmann, Andreas T1 - Degrees-of-freedom penalized piecewise regression JF - Information and Inference: A Journal of the IMA N2 - 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. 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 that 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. Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:863-opus-57846 SN - 2049-8772 VL - 14 IS - 1 PB - Oxford University Press ER - TY - CHAP A1 - Selig, Tim A1 - Bauer, Patrick A1 - Frikel, Jürgen A1 - März, Thomas A1 - Storath, Martin A1 - Weinmann, Andreas T1 - Two-stage Approach for Low-dose and Sparse-angle CT Reconstruction using Backprojection T2 - Informatik aktuell Y1 - 2025 SN - 9783658474218 U6 - https://doi.org/10.1007/978-3-658-47422-5_67 SN - 1431-472X SP - 286 EP - 291 PB - Springer Fachmedien Wiesbaden CY - Wiesbaden ER - TY - CHAP A1 - Storath, Martin A1 - Weinmann, Andreas T1 - Solving higher-order Mumford-Shah models T2 - INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: ICNAAM2022 Y1 - 2024 U6 - https://doi.org/10.1063/5.0210598 SN - 0094-243X PB - AIP Publishing ER - TY - JOUR A1 - Storath, Martin A1 - Weinmann, Andreas T1 - Smoothing Splines for Discontinuous Signals JF - Journal of Computational and Graphical Statistics Y1 - 2023 U6 - https://doi.org/10.1080/10618600.2023.2262000 SN - 1061-8600 VL - 33 IS - 2 SP - 651 EP - 664 PB - Informa UK Limited ER -