Robusne metode optimizacije u strojnom učenju

master's thesis

• Title (english): Robust optimization methods in machine learning
• Author: Martina Čuklić
• Mentor: Marko Vrdoljak (mentor)
• Committee member: Marko Vrdoljak (predsjednik povjerenstva)
• Committee member: Marko Erceg (član povjerenstva)
• Committee member: Matej Mihelčić (član povjerenstva)
• Committee member: Ivica Nakić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-03-02, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu prikazali smo primjene nekih tehnika robusne optimizacije u strojnom učenju. Robusna optimizacija važan je dio optimizacije koji se bavi nesigurnošću u podacima optimizacijskih problema. Kako se u današnje vrijeme strojno učenje često susreće s nesigurnošću, robusna optimizacija tu ima sve veću ulogu. Promatrana je veza između robusnosti i regulariziranog stroja potpornih vektora, točnije, pokazali smo da je standardni regularizirani stroj potpornih vektora posebni slučaj robusne optimizacije. Zatim je uvedena robusna regresija s pogreškom najmanjih kvadrata te je promatran slučaj gdje su značajke izložene smetnjama, to jest nesigurnosti. Osigurana je interpretacija Lasso algoritma s robusne perspektive, a na temelju te robusne interpretacije istražena su svojstva rijetkosti i konzistentnosti. Osim toga, predstavljen je rezultat koji nam govori da su rijetkost i stabilnost u kontradikciji, to jest da se ne mogu postići simultano.

Abstract (english)

In this paper, we presented some robust optimization techniques in machine learning. Robust optimization is an important part of optimization that deals with uncertainty in the data of optimization problems. As today’s machine learning is often faced with uncertainty, robust optimization plays an increasingly important role. The connection between robustness and regularized support vector machine was observed, more precisely, we showed that the standard regularized support vector machine is a special case of robust optimization. Robust regression with least squares error was introduced and the case where the features are exposed to disturbances, that is, uncertainties, was observed. An interpretation of the Lasso algorithm from a robust perspective is provided, and on the basis of this robust interpretation, the properties of sparsity and consistency are investigated. In addition, a result is presented that tells us that sparsity and stability are in contradiction, that is, they cannot be achieved simultaneously.

• Keywords: nesigurnostu u podacima optimizacijskih problema; standardni regularizirani stroj potpornih vektora; Lasso algoritam
• Keywords (english): uncertainty in the data of optimization problems; standard regularized support vector machine; Lasso algorithm
• Language: croatian
• URN:NBN: urn:nbn:hr:217:384663
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2023-03-23 15:10:03