A regression tree approach using mathematical programming

Lingjian Yang,Songsong Liu,Sophia Tsoka,Lazaros G Papageorgiou

doi:10.1016/j.eswa.2017.02.013

Abstract

Regression analysis is a machine learning approach that aims to accurately predict the value of continuous output variables from certain independent input variables, via automatic estimation of their latent relationship from data. Tree-based regression models are popular in literature due to their flexibility to model higher order non-linearity and great interpretability. Conventionally, regression tree models are trained in a two-stage procedure, i.e. recursive binary partitioning is employed to produce a tree structure, followed by a pruning process of removing insignificant leaves, with the possibility of assigning multivariate functions to terminal leaves to improve generalisation. This work introduces a novel methodology of node partitioning which, in a single optimisation model, simultaneously performs the two tasks of identifying the break-point of a binary split and assignment of multivariate functions to either leaf, thus leading to an efficient regression tree model. Using six real world benchmark problems, we demonstrate that the proposed method consistently outperforms a number of state-of-the-art regression tree models and methods based on other techniques, with an average improvement of 7–60% on the mean absolute errors (MAE) of the predictions.

Highlights

Regression analysis seeks to estimate the relationships between output variables and a set of independent input variables by automatically learning from a number of curated samples (Sen & Srivastava, 2012)
We have proposed a novel regression tree learning algorithm, named Mathematical Programming Tree (MPTree)
An optimisation model OPLRA recently published in literature has been adopted to optimise the binary node splitting

Summary

Introduction

Regression analysis seeks to estimate the relationships between output variables and a set of independent input variables by automatically learning from a number of curated samples (Sen & Srivastava, 2012). The primary goal of applying a regression analysis is usually to obtain precise prediction of the level of output variables for new samples. One would like to gain some useful insights into the underlying relationship between the input and output variables, in which case the interpretability of a regression method is of great interest. Regression tree is a type of the machine learning tools that can satisfy both good prediction accuracy and easy interpretation, and have received extensive attention in the literature. A regression model is fitted to each terminal node to get the predicted values of the output variables of new samples

Objectives

Methods

Results

Conclusion