Abstract
Shape constrained spline fitting is a useful method to impose prior knowledge onto flexible semi-parametric models during parameter estimation. Most typically, the function shape is imposed through order restrictions on the regression coefficients. The intended shape is considered known or selected based on heuristic rules. In this study, we present a method to estimate the optimal set of order restrictions to segment a univariate data series into episodes with distinct shapes. This is also known as the qualitative trend analysis (QTA) problem. The obtained solution uses a trade-off between lack-of-fit and model complexity. Our practical implementation takes inspiration from the generalized order restricted information criterion (GORIC) for inequality-constrained model selection. From this, one learns (a) that QTA can be formulated as a mixed-integer quadratic program (MIQP) and (b) that the newly proposed mixed order restricted information criterion (MORIC) enables optimal segmentation. This is illustrated through didactic case studies.
| Original language | English |
|---|---|
| Article number | 108109 |
| Journal | Computers and Chemical Engineering |
| Volume | 170 |
| DOIs | |
| State | Published - Feb 2023 |
Funding
This research is sponsored by the US Department of Energy (DOE) , Office of Energy Efficiency and Renewable Energy , Advanced Manufacturing Office , under contract DE-AC05-00OR22725 with UT-Battelle LLC. This manuscript has been authored by UT-Battelle LLC under contract DE-AC05-00OR22725 with DOE. The US government retains—and the publisher, by accepting the article for publication, acknowledges that the US government retains—a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript or allow others to do so for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( http://energy.gov/downloads/doe-public-access-plan ). This research used resources of the Compute and Data Environment for Science (CADES) at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725 . This research is sponsored by the US Department of Energy (DOE), Office of Energy Efficiency and Renewable Energy, Advanced Manufacturing Office, under contract DE-AC05-00OR22725 with UT-Battelle LLC. This manuscript has been authored by UT-Battelle LLC under contract DE-AC05-00OR22725 with DOE. The US government retains—and the publisher, by accepting the article for publication, acknowledges that the US government retains—a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript or allow others to do so for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). This research used resources of the Compute and Data Environment for Science (CADES) at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.
Keywords
- Model selection
- Order restricted regression
- Qualitative representation
- Shape constraints
- Time series segmentation
- Truncated distribution