Robust optimal classification trees under noisy labels

Victor Blanco,Justo Puerto,Alberto Japón

doi:10.1007/s11634-021-00467-2

Victor Blanco, Justo Puerto + Show 1 more

Open Access

https://doi.org/10.1007/s11634-021-00467-2

Copy DOI

Abstract

In this paper we propose a novel methodology to construct Optimal Classification Trees that takes into account that noisy labels may occur in the training sample. The motivation of this new methodology is based on the superaditive effect of combining together margin based classifiers and outlier detection techniques. Our approach rests on two main elements: (1) the splitting rules for the classification trees are designed to maximize the separation margin between classes applying the paradigm of SVM; and (2) some of the labels of the training sample are allowed to be changed during the construction of the tree trying to detect the label noise. Both features are considered and integrated together to design the resulting Optimal Classification Tree. We present a Mixed Integer Non Linear Programming formulation for the problem, suitable to be solved using any of the available off-the-shelf solvers. The model is analyzed and tested on a battery of standard datasets taken from UCI Machine Learning repository, showing the effectiveness of our approach. Our computational results show that in most cases the new methodology outperforms both in accuracy and AUC the results of the benchmarks provided by OCT and OCT-H.

Highlights

Discrete Optimization has experienced a tremendous growth in the last decades, both in its theoretical and practical sides, partially provoked by the emergence of new computational resources as well as real-world applications that have boosted this growth
In this paper we propose a novel binary supervised classification method, called Optimal Classification Tree with Support Vector Machines (OCTSVM), that profits both from the ideas of SVM and Optimal Classification Trees (OCT) to build classification rules
Notice that OCT+SVM is a modification of our OCTSVM in which the ξit variables are fixed to zero, i.e., no relabeling is allowed in the model

Summary

Introduction

Discrete Optimization has experienced a tremendous growth in the last decades, both in its theoretical and practical sides, partially provoked by the emergence of new computational resources as well as real-world applications that have boosted this growth. This impulse has motivated the use of Discrete Optimization models to deal with problems involving a large number of variables and constraints, that years before would have not been possible to be dealt with. The development of robust methods against these kind of problems has attracted the attention of researchers (see e.g., Bertsimas et al (2019); Blanco et al (2020b))

Objectives

Methods

Findings

Conclusion