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Piecewise Regression through the Akaike Information Criterion using Mathematical Programming

Gkioulekas, I; Papageorgiou, LG; (2018) Piecewise Regression through the Akaike Information Criterion using Mathematical Programming. In: IFAC-PapersOnLine. (pp. pp. 730-735). Elsevier Green open access

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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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