Doğrusal Regresyonda Aykırı Değer Tespit Algoritmaları için Dayanıklı Bir Temel Küme Seçim Yöntemi

Year 2024, Issue: 10, 76 - 85

Mehmet Hakan Satman

https://doi.org/10.52693/jsas.1512794

Abstract

Bu çalışmanın temel motivasyonu, makul bir kirlilik seviyesine kadar doğrusal regresyonda aykırı değerlerin teşhisi ve tespiti için etkili bir algoritma geliştirmektir. Algoritma başlangıçta doğrusal cebir düzeyinde şapka matrisinin sağlam bir versiyonunu elde eder. İlk aşamada elde edilen temel alt küme, hızlı LTS (Least Trimmed Squares) regresyon algoritmasında tanımlandığı gibi konsantrasyon adımlarıyla iyileştirilir. Yöntem, temel alt küme seçim durumu olarak başka bir algoritmaya takılabilir. Algoritma hem X hem de Y yönündeki aykırı değerlere karşı %25 oranında etkilidir. Algoritmanın karmaşıklığı gözlem ve parametre sayısı ile doğrusal olarak artmaktadır. Algoritma iteratif hesaplamalar gerektirmediği için oldukça hızlıdır. Algoritmanın belirli bir kirlilik seviyesine karşı başarısı simülasyonlarla gösterilmiştir.

Keywords

doğrusal regresyon, aykırı değerler, dayanıklı regresyon

A Robust Initial Basic Subset Selection Method for Outlier Detection Algorithms in Linear Regression

Abstract

The main motivation of this study is to develop an efficient algorithm for diagnosing and detecting outliers in linear regression up to a reasonable level of contamination. The algorithm initially obtains a robust version of the hat matrix at the linear algebra level. The basic subset obtained in the first stage is improved through concentration steps as defined in the fast-LTS (Least Trimmed Squares) regression algorithm. The method can be plugged into another algorithm as a basic subset selection state. The algorithm is effective against outliers in both X and Y directions by a rate of 25%. The complexity of the algorithm increases linearly with the number of observations and parameters. The algorithm is quite fast as it does not require iterative calculations. The success of the algorithm against a specific contamination level is demonstrated through simulations.

Keywords

Linear regression, outlier detection, robust regression

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