Metoda parcijalnih najmanjih kvadrata

master's thesis

• Title (english): Method of partial least squares
• Author: Sanjin Jurić Fot
• Mentor: Azra Tafro (mentor)
• Committee member: Azra Tafro (predsjednik povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Committee member: Vedran Čačić (član povjerenstva)
• Committee member: Ilja Gogić (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

Metoda parcijalnih najmanjih kvadrata (PLS) statistička je metoda koja se koristi za analizu odnosa dvaju slučajnih veličina \( {x}\) i \({y}\), najčešće za predviđanje \( {y}\) preko \( {x}\). Slična je analizi glavnih komponenata (PCA), utoliko što se obje metode bave smanjenjem dimenzije, tj. pronalaze skup novih nekoreliranih varijabli koje će sadržavati maksimalno informacija o početnima; ali za razliku od PCA-a, koji pronalazi komponente za maksimalno objašnjenje varijance u \( {x}\), komponente nastale PLS-om objašnjavaju varijancu u obje veličine, te se stoga mogu koristiti kao ulazi u neki prediktivni model, kao što je linearna regresija. Metoda parcijalnih najmanjih kvadrata posebno je korisna kada je omjer broja opažanja i dimenzije od \( {x}\) malen te kada su kovarijate visoko korelirane. U ovom smo radu opisali metodu i izveli ključne teorijske rezultate vezane uz nju te pokazali kako ona u određenim slučajevima predviđa bolje od linearne regresije i regresije na glavnim komponentama.

Abstract (english)

Partial least squares (PLS) is a statistical method used for analyzing the relationship between two random variables \({x}\) and \({y}\), most commonly to predict \({y}\) from \({x}\). It is similar to principal components analysis (PCA) - both methods deal with dimension reduction, i.e. they construct a set of new uncorrelated variables that will contain maximum information about the initial ones; but unlike PCA, which finds the components that maximally explain the variance in \({x}\), the components generated by PLS explain the variance in both variables, and can therefore be used as inputs to some predictive model, such as linear regression. PLS is especially useful when the ratio of the number of observations to the dimension of \({x}\) is small and when the explanatory variables are highly correlated. In this paper we described the method, derived crucial theoretical results related to it, and showed that in certain cases it performs better than linear regression and principal component regression (PCR).

• Keywords: statističke metode; analiza glavnih komponenata (PCA); prediktivni model; linearna regresija
• Language: croatian
• URN:NBN: urn:nbn:hr:217:618422
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-02-12 08:39:16