Outlier Detection in Multiple Regression Models Using Genetic Algorithms and Bayesian Information Criteria

Öz

Statistical models, particularly regression models, are most useful devices for extracting and understanding the essential features of datasets. However, most of the databases in real-world include a particular amount of abnormal values, generally termed as outliers. An accurate identification of outliers plays a significant role in statistical analysis especially regression models. Nevertheless, many classical statistical models are blindly applied to data sets containing outliers, the results can be misleading at best. The appearance of outliers can exert negative influences on the fit of the multiple regression models. The aim of this study is to define outlier detection method using Genetic Algorithms (GA) with Bayesian Information Criterion (BIC) and to illustrate the algorithm with real and simulation data. We use a fitness function which is based on BIC in this algorithm. The criteria’s value indicates a better model to fit data, the presence of one or more outliers will negatively impact the regression model and result in larger BIC values.

Anahtar Kelimeler

• Bayesian information criterion
• Genetic algorithms
• Multiple regression models
• Outlier detection

Çoklu Regresyon Modellerinde Genetik Algoritma ve Bayes Bilgi Kriteri Kullanarak Sapan Değerlerin Belirlenmesi

Öz

İstatistiksel modeller; özellikle regresyon modelleri, veri setlerinin önemli özelliklerinin anlaşılması ve ortaya çıkarılmasında en çok kullanılan araçlardandır. Bununla birlikte, gerçek hayatta birçok veri seti genellikle sapan değer olarak adlandırılan belirli miktardaki anormal değerler içerebilmektedir. Sapan değerlerin doğru bir şekilde tespit edilmesi, istatistiksel çözümlemelerde özellikle de regresyon modellerinde önemli bir rol oynar. Buna rağmen, birçok klasik istatistiksel modeller sapan değer içeren veri setlerine de uygulanmakta, nihayetinde de sonuçlar yanıltıcı olmaktadır. Sapan değerler, uygun olan çoklu regresyon modelinin belirlenmesini de güçleştirir.

Bu çalışmanın amacı, Genetik Algoritma (GA) ve Bayes Bilgi Kriteri (BIC) kullanarak sapan değer belirleme yöntemini tanımlamak ve algoritmayı gerçek ve benzetim verisi ile göstermektir. Genetik algoritmada BIC tabanlı uygunluk fonksiyonu kullanılmıştır. BIC değeri, veri için en uygun modeli göstermekte olup, bir veya daha çok sapan değerin varlığında regresyon modeli bu gözlemlerden olumsuz yönde etkilenecek ve daha büyük BIC değerli sonuçlar verecektir.

Anahtar Kelimeler

• Bayes bilgi kriteri
• Genetik algoritmalar
• Çoklu regresyon modelleri
• Sapan değer belirleme

Kaynakça

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