Parameter estimation in generalized partial linear models with conic quadratic programming
Genelleştirilmiş parçalı doğrusal modellerde ikinci dereceden konik karesel programlama yöntemi ile parametre tahmini
- Tez No: 275853
- Danışmanlar: PROF. DR. BÜLENT KARASÖZEN, PROF. DR. GERHARD WİLHELM WEBER
- Tez Türü: Yüksek Lisans
- Konular: Matematik, İstatistik, Mathematics, Statistics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2010
- Dil: İngilizce
- Üniversite: Orta Doğu Teknik Üniversitesi
- Enstitü: Uygulamalı Matematik Enstitüsü
- Ana Bilim Dalı: Bilimsel Hesaplama Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 117
Özet
Özet yok.
Özet (Çeviri)
In statistics, regression analysis is a technique, used to understand and model therelationship between a dependent variable and one or more independent variables.Multiple Adaptive Regression Spline (MARS) is a form of regression analysis. It is anon-parametric regression technique and can be seen as an extension of linear modelsthat automatically models non-linearities and interactions. MARS is very importantin both classification and regression, with an increasing number of applications inmany areas of science, economy and technology.In our study, we analyzed Generalized Partial Linear Models (GPLMs), which areparticular semiparametric models. GPLMs separate input variables into two partsand additively integrates classical linear models with nonlinear model part. In orderto smooth this nonparametric part, we use Conic Multiple Adaptive Regression Spline(CMARS), which is a modified form of MARS. MARS is very benefical for highdimensional problems and does not require any particular class of relationship betweenthe regressor variables and outcome variable of interest. This technique offers a great advantage for fitting nonlinear multivariate functions. Also, the contribution of thebasis functions can be estimated by MARS, so that both the additive and interactioneffects of the regressors are allowed to determine the dependent variable. There aretwo steps in the MARS algorithm: the forward and backward stepwise algorithms. Inthe first step, the model is constructed by adding basis functions until a maximumlevel of complexity is reached. Conversely, in the second step, the backward stepwisealgorithm reduces the complexity by throwing the least significant basis functions fromthe model.In this thesis, we suggest not using backward stepwise algorithm, instead, we employa Penalized Residual Sum of Squares (PRSS). We construct PRSS for MARS as aTikhonov Regularization Problem. We treat this problem using continuous optimizationtechniques which we consider to become an important complementary technologyand alternative to the concept of the backward stepwise algorithm. Especially, we applythe elegant framework of Conic Quadratic Programming (CQP) an area of convexoptimization that is very well-structured, hereby, resembling linear programming and,therefore, permitting the use of interior point methods.At the end of this study, we compare CQP with Tikhonov Regularization problemfor two different data sets, which are with and without interaction effects. Moreover,by using two another data sets, we make a comparison between CMARS and twoother classification methods which are Infinite Kernel Learning (IKL) and TikhonovRegularization whose results are obtained from the thesis, which is on progress.
Benzer Tezler
- Advances in robust identification of spline models and networks by robust conic optimization, with applications to different sectors
Değişik sektörlere uygulamalarıyla birlikte sağlam konik optimizasyon ile eğri modelleri ve ağların sağlam tanımlanmasındaki gelişimler
AYŞE ÖZMEN
Doktora
İngilizce
2015
MatematikOrta Doğu Teknik ÜniversitesiBilimsel Hesaplama Ana Bilim Dalı
PROF. DR. GERHARD WİEHELM WEBER
- Refinements, extensions and modern applications of conic multivariate adaptive regression splines
Konik çok değişkenli uyarlanabilir regresyon eğrilerinin geliştirilmesi, uzantıları ve modern uygulamaları
FATMA YERLİKAYA ÖZKURT
Doktora
İngilizce
2013
MatematikOrta Doğu Teknik ÜniversitesiBilimsel Hesaplama Ana Bilim Dalı
PROF. DR. GERHARD WILHELM WEBER
- Parameter estimation in generalized partial linear models with tikhanov regularization
Genelleştirilmiş parçalı doğrusal modellerde tikhanov düzenleme ile parametre tahmini
BELGİN KAYHAN
Yüksek Lisans
İngilizce
2010
MatematikOrta Doğu Teknik ÜniversitesiBilimsel Hesaplama Ana Bilim Dalı
PROF. DR. BÜLENT KARASÖZEN
PROF. DR. GERHARD WİLHELM WEBER
- Sales forecasting in fashion retail industry with classical and machine learning methods
Moda perakendesi sektöründe klasik ve makine öğrenmesi metodları ile satış tahmini
HANİFE IŞIK
Yüksek Lisans
İngilizce
2020
Ekonomiİstanbul Teknik ÜniversitesiEkonomi Ana Bilim Dalı
DOÇ. DR. TOLGA YURET
