prikaz prve stranice dokumenta Gradijentne metode bezuvjetne minimizacije
No public access
undergraduate thesis
Gradijentne metode bezuvjetne minimizacije
Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing, 2020. urn:nbn:hr:168:288150
Hubak, Karlo
University of Zagreb
Faculty of Electrical Engineering and Computing

Institutional repository: FER Repository

Cite this document

Hubak, K. (2020). Gradijentne metode bezuvjetne minimizacije (Undergraduate thesis). Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing. Retrieved from https://urn.nsk.hr/urn:nbn:hr:168:288150

Hubak, Karlo. "Gradijentne metode bezuvjetne minimizacije." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2020. https://urn.nsk.hr/urn:nbn:hr:168:288150

Hubak, Karlo. "Gradijentne metode bezuvjetne minimizacije." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2020. https://urn.nsk.hr/urn:nbn:hr:168:288150

Hubak, K. (2020). 'Gradijentne metode bezuvjetne minimizacije', Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, accessed 17 July 2024, https://urn.nsk.hr/urn:nbn:hr:168:288150

Hubak K. Gradijentne metode bezuvjetne minimizacije [Undergraduate thesis]. Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing; 2020 [cited 2024 July 17] Available at: https://urn.nsk.hr/urn:nbn:hr:168:288150

K. Hubak, "Gradijentne metode bezuvjetne minimizacije", Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:168:288150

Metadata
TitleGradijentne metode bezuvjetne minimizacije
Title (english)Gradient-based algorithms for unconstrained minimization
AuthorKarlo Hubak
MentorJosipa Pina Milišić (mentor)
Committee memberJosipa Pina Milišić (predsjednik povjerenstva)
Committee memberMario Krnić (član povjerenstva)
Committee memberAnamari Nakić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Electrical Engineering and Computing
Zagreb
Defense date and country2020-09-15, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Computing
Abstract
Gradijentni algoritmi su često korištene metode prilikom riješavanja problema bezuvjetne minimizacije. Poznavajući gradijent funkcije koja je objekt optimizacije, svaka iteracija gradijentnog algoritma teži minimumu dane funkcije. U vrijeme kada algoritmi koji služe za predviđanje (u koje se ubrajaju i gradijentni algoritmi) često trebaju baratati s količinama podataka na razini web-a, mnogi algoritmi mogu postati neprikladni, no, kako raste količina podataka, tako raste i naša sposobnost da ih precizno interpretiramo. Najprije, dana je matematička osnova gradijentnih metoda, a zatim su pokazane performanse dva različita gradijentna algoritma: gradijentni spust (GS) i stohastički gradijentni spust (SGS). Razmotren je sintetizirani model linearne regresije. Performanse algoritama su evaluirane procjenom najveće izglednosti. Nakon toga, analiza konvergencije je prikazana. Na kraju, SGS je pokretan nad sve većim podskupovima podataka. Takvi podskupovi se nazivaju mini-grupe. U slučaju linearne regresije, pokazano je da SGS ima bolje performanse od GS-a kako se količina podataka povećava. Nadalje, kako se povećava veličina mini-grupa, preciznost SGS-a ne raste značajno.
Abstract (english)
Gradient-based algorithms are popular when solving unconstrained optimization problems. By exploiting knowledge of the gradient of the objective function to optimize, each iteration of a gradient-based algorithm aims at approaching the minimizer of said function. In this age, when prediction algorithms (of which gradient-based algorithms are a part of), many algorithms may encounter difficulties. However, as the data sets grow larger, so does our capability to interpret them. Firstly, the basis of mathematics background is covered concerning gradient optimization, after that the performance of two different gradient-based algorithms, Gradient Descent (GD) and Stochastic Gradient Descent (SGD) is presented. A synthetic linear regression model is considered. Performance of the algorithms are evaluated by comparison with the maximum likelihood estimator (MLE). Thereafter, a convergence study is presented. Lastly, SGD is evaluated over increasingly large, random subsets of the data. Such a subset is known as a mini-batch. In the case of linear regression, it is found that SGD outperforms GD as the data sets grow larger. Furthermore, the precision of SGD does not necessarily improve when increasing the mini-batch size.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:168:288150
Study programmeTitle: Computing
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
Type of resourceText
File originBorn digital
Access conditionsClosed access
Terms of useLicence In copyright icon
Public note
Created on2023-01-13 10:04:04