Risk-averse multi-class support vector machines
Author(s)
Advisor
İyigün, Özlem ÇavuşDate
2018-12Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
312
views
views
171
downloads
downloads
Abstract
A classification problem aims to identify the class of new observations based on
the previous observations whose classes are known. It has many applications in a
variety of disciplines such as medicine, finance and artificial intelligence. However,
presence of outliers and noise in previous observations may have significant impact
on the classification performance. Support vector machine (SVM) is a classifier
introduced to solve binary classification problems under the presence of noise and
outliers. In the literature, risk-averse SVM is shown to be more stable to noise and
outliers compared to the original SVM formulations. However, we often observe
more than two classes in real-life datasets. In this study, we aim to develop riskaverse
multi-class SVMs following the idea of risk-averse binary SVM. We use
risk measures, VaR and CVaR, to implement risk-aversion to multi-class SVMs.
Since VaR constraints are nonconvex in general, SVMs with VaR constraints are
more complex than SVMs with CVaR. Therefore, we propose a strong big-M
formulation to solve multi-class SVM problems with VaR constraints efficiently.
We also provide a computational study on the classification performance of the
original multi-class SVM formulations and the proposed risk-averse formulations
using artificial and real-life datasets. The results show that multi-class SVMs
with VaR are more stable to outliers and noise compared to multi-class SVMs
with CVaR, and both of them are more stable than the original formulations.
Keywords
Support Vector MachinesMulti-Class Classification Problem
Riskaversion
Conditional Value-at-Risk
Value-at-Risk