Gkioulekas, I;
Papageorgiou, LG;
(2018)
Piecewise Regression through the Akaike Information Criterion using Mathematical Programming.
In:
IFAC-PapersOnLine.
(pp. pp. 730-735).
Elsevier
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Abstract
In machine learning, regression analysis is a tool for predicting the output variables from a set of known independent variables. Through regression analysis, a function that captures the relationship between the variables is fitted to the data. Many methods from literature tackle this problem with various degrees of difficulty. Some simple methods include linear regression and least squares, while some are more complicated such as support vector regression. Piecewise or segmented regression is a method of analysis that partitions the independent variables into intervals and a function is fitted to each interval. In this work, the Optimal Piecewise Linear Regression Analysis (OPLRA) model is used from literature to tackle the problem of segmented analysis. This model is a mathematical programming approach that is formulated as a mixed integer linear programming problem that optimally partitions the data into multiple regions and calculates the regression coefficients, while minimising the Mean Absolute Error of the fitting. However, the number of regions is a known priori. For this work, an extension of the model is proposed that can optimally decide on the number of regions using information criteria. Specifically, the Akaike Information Criterion is used and the objective is to minimise its value. By using the criterion, the model no longer needs a heuristic approach to decide on the number of regions and it also deals with the problem of overfitting and model complexity.
| Type: | Proceedings paper |
|---|---|
| Title: | Piecewise Regression through the Akaike Information Criterion using Mathematical Programming |
| Event: | 18th IFAC Symposium on System Identification (SYSID) |
| Location: | Stockholm Univ, AlbaNova Univ Ctr, Stockholm, SWEDEN |
| Dates: | 09 July 2018 - 11 July 2018 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.ifacol.2018.09.168 |
| Publisher version: | https://doi.org/10.1016/j.ifacol.2018.09.168 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Mathematical programming, Regression analysis, Optimisation, Information criterion, Machine learning |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Chemical Engineering |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10064156 |
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