Wednesday, October 20, 2010

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naive Bayesian continuous predictors

The classifier Naive Bayes is a supervised learning method based on a strong simplifying assumption: the descriptors (Xj) are pairwise conditionally independent values of the variable to predict (Y). Yet despite this, it proves robust and efficient. Its performance is comparable to other learning techniques. Various reasons are advanced in the literature. We ourselves proposed an explanation based on bias of representation in a previous tutorial. When predictors are discrete, one realizes easily that the naive Bayesian classifier is a linear separator. It arises in direct competition with other techniques of the same ilk, such as discriminant analysis, logistic regression, SVM (Support Vector Machine) linear, etc..

In this tutorial, we describe the model of conditional independence within the framework of quantitative predictor variables. The situation is somewhat more complex. We shall see that the simplifying assumptions used, it can be considered as a linear or quadratic separator. It is then possible to produce a classifier explicit, easy to use for deployment. The ideas put forward in this tutorial have been implemented in Tanagra 1.4.37 (and later). This representation model is original. I have not found in other free software that I used to follow (for now ...).

This paper is organized as follows. Firstly (Section 2), we detail the theoretical aspects of the method. We show that it is possible to reach an explicit model that can be expressed as a linear combination of variables or variables of the square. In Section 3, we describe the implementation of the method using the software Tanagra. We compare the results with those of other separators linear (logistic regression, linear SVM, PLS discriminant analysis, discriminant analysis of Fisher). In Section 4, we compare the implementation of technology in various software. We will mainly focus on reading the results. Finally, Section 5, we show the usefulness of the approach on very large files. We will cover the basic "mutants" comprising 16,592 observations Predictors and 5408 with a speed beyond the reach of other techniques.

Keywords: Bayesian classifier naive model of conditional independence, 5.0.10 RapidMiner, Weka 3.7.2, 2.2.2 Knime, software R package e1071, discriminant analysis, PLS discriminant analysis, PLS regression, svm linear regression
Components: NAIVE BAYES CONTINUOUS, BINARY LOGISTIC REGRESSION, SVM, C-PLS, LINEAR DISCRIMINANT ANALYSIS
Tutorial: fr_Tanagra_Naive_Bayes_Continuous_Predictors.pdf
Data : breast ; Low Birth Weight
References:
Wikipedia, "Naive Bayes classification "
Tanagra, " Naïve Bayes classifier for discrete predictors "

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