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Piecewise regression analysis through information criteria using mathematical programming
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DOI：10.1016/j.eswa.2018.12.013.png)
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摘要
En 中文
Regression is a predictive analysis tool that examines the relationship between independent and dependent variables. The goal of this analysis is to fit a mathematical function that describes how the value of the response changes when the values of the predictors vary. The simplest form of regression is linear regression which in the case multiple regression, tries to explain the data by simply fitting a hyperplane minimising the absolute error of the fitting. Piecewise regression analysis partitions the data into multiple regions and a regression function is fitted to each one. Such an approach is the OPLRA (Optimal Piecewise Linear Regression Analysis) model (Yang, Liu, Tsoka, & Papage, 2016) which is a mathematical programming approach that optimally partitions the data into multiple regions and fits a linear regression functions minimising the Mean Absolute Error between prediction and truth. However, using many regions to describe the data can lead to overfitting and bad results. In this work an extension of the OPLRA model is proposed that deals with the problem of selecting the optimal number of regions as well as overfitting. To achieve this result, information criteria such as the Akaike and the Bayesian are used that reward predictive accuracy and penalise model complexity. (C) 2018 Published by Elsevier Ltd.
Keyword:
Mathematical programming
Regression analysis
Optimisation
Information criterion
Machine learning
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期刊
IF:
7.5
论文数:
3.0W
被引数:
10.2W
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