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AKILLI SİSTEMLER VE UYGULAMALARI DERGİSİ
JOURNAL OF INTELLIGENT SYSTEMS WITH APPLICATIONS
J. Intell. Syst. Appl.
E-ISSN: 2667-6893
Creative Commons License This work is licensed under a Creative Commons Attribution 4.0 International License.

Modification of posterior probability variable with frequency factor according to Bayes Theorem

Bayes Teoremine göre frekans faktörü ile arka olasılık değişkeninin modifikasyonu

How to cite: Vural MS, Telçeken M. Modification of posterior probability variable with frequency factor according to bayes theorem. Akıllı Sistemler ve Uygulamaları Dergisi (Journal of Intelligent Systems with Applications) 2022; 5(1): 19-26. DOI: 10.54856/jiswa.202205195

Full Text: PDF, in English.

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Title: Modification of posterior probability variable with frequency factor according to Bayes Theorem

Abstract: Probability theory is a branch of science that statistically analyzes random events. Thanks to this branch of science, machine learning techniques are used inferences for the prediction or recommendation system. One of the statistical methods at the forefront of these techniques is Bayesian theory. Bayes is a simple mathematical formula used to calculate conditional probabilities and obtain the best estimates. The two most important parts of the formula are the concepts of a priori probability and posterior/conditional probability. In a priori probability, the most rational assessment of the probability of an outcome is made based on the available data, while in posterior probability, the probability of the event occurring is calculated after considering all evidence or data. In this study, a new mathematical model is presented to calculate the posterior probability variable of Bayesian theory more precisely. According to this new mathematical model, equal priority probabilities of some variables should be recalculated according to frequency. Calculations are applied to two nodes. The first of these two nodes is the node consisting of the existing data, and the second is the queried node. The positive frequency value will be applied when the variables consisting of existing data and having the same a priori probabilities are found at the questioned node, and negative frequency value will be applied for the other variables. Thus, while calculating a standard probability value according to Bayesian Theory, frequency-based values are taken into account with the help of the newly created mathematical model. With the help of these frequencies, the modification of the system reveals more precise results according to these two basic principles. The results obtained were tested with the cross validation method and high accuracy rates were determined.

Keywords: Bayesian Theory, Machine şearning, Mathematical model


Başlık: Bayes Teoremine göre frekans faktörü ile arka olasılık değişkeninin modifikasyonu

Özet: Olasılık teorisi, rastgele olayları istatistiksel olarak analiz eden bir bilim dalıdır. Bu bilim dalı sayesinde makine öğrenmesi teknikleri tahmin veya öneri sistemi için çıkarımlarda kullanılmaktadır. Bu tekniklerin başında istatistiksel yöntemlerden biri Bayes teorisidir. Bayes, koşullu olasılıkları hesaplamak ve en iyi tahminleri elde etmek için kullanılan basit bir matematiksel formüldür. Formülün en önemli iki kısmı, önsel olasılık ve sonsal/koşullu olasılık kavramlarıdır. Önsel olasılıkta, bir sonucun olasılığının en rasyonel değerlendirmesi mevcut verilere dayalı olarak yapılırken, sonraki olasılıkta olayın meydana gelme olasılığı tüm kanıtlar veya veriler dikkate alınarak hesaplanır. Bu çalışmada, Bayes teorisinin sonsal olasılık değişkenini daha kesin olarak hesaplamak için yeni bir matematiksel model sunulmaktadır. Bu yeni matematiksel modele göre bazı değişkenlerin eşit öncelikli olasılıkları frekansa göre yeniden hesaplanmalıdır. Hesaplamalar iki düğüme uygulanır. Bu iki düğümden ilki mevcut verilerden oluşan düğüm, ikincisi ise sorgulanan düğümdür. Mevcut verilerden oluşan ve aynı a priori olasılıklara sahip değişkenler sorgulanan düğümde bulunduğunda pozitif frekans değeri, diğer değişkenler için negatif frekans değeri uygulanacaktır. Böylece Bayes Teorisine göre standart bir olasılık değeri hesaplanırken yeni oluşturulan matematiksel model yardımıyla frekans bazlı değerler dikkate alınmaktadır. Bu frekanslar yardımıyla sistemin modifikasyonu bu iki temel prensibe göre daha kesin sonuçlar ortaya koymaktadır. Elde edilen sonuçlar çapraz doğrulama yöntemi ile test edilmiş ve yüksek doğruluk oranları belirlenmiştir.

Anahtar kelimeler: Bayes Teorisi, Makine öğrenme, Matematiksel model


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