Editing Naive Bayes classifier (section)

==Introduction==
Naive Bayes is a simple technique for constructing classifiers: models that assign class labels to problem instances, represented as vectors of [[feature vector|feature]] values, where the class labels are drawn from some finite set. There is not a single [[algorithm]] for training such classifiers, but a family of algorithms based on a common principle: all naive Bayes classifiers assume that the value of a particular feature is [[Independence (probability theory)|independent]] of the value of any other feature, given the class variable. For example, a fruit may be considered to be an apple if it is red, round, and about 10&nbsp;cm in diameter.  A naive Bayes classifier considers each of these features to contribute independently to the probability that this fruit is an apple, regardless of any possible [[Correlation and dependence|correlations]] between the color, roundness, and diameter features.

In many practical applications, parameter estimation for naive Bayes models uses the method of [[maximum likelihood]]; in other words, one can work with the naive Bayes model without accepting [[Bayesian probability]] or using any Bayesian methods.

Despite their naive design and apparently oversimplified assumptions, naive Bayes classifiers have worked quite well in many complex real-world situations. In 2004, an analysis of the Bayesian classification problem showed that there are sound theoretical reasons for the apparently implausible [[efficacy]] of naive Bayes classifiers.<ref>{{cite conference | first = Harry | last = Zhang | title = The Optimality of Naive Bayes | conference = FLAIRS2004 conference | url = http://www.cs.unb.ca/profs/hzhang/publications/FLAIRS04ZhangH.pdf }}</ref> Still, a comprehensive comparison with other classification algorithms in 2006 showed that Bayes classification is outperformed by other approaches, such as [[boosted trees]] or [[random forests]].<ref>{{cite conference | last1 = Caruana | first1 = R. | last2 = Niculescu-Mizil | first2 = A. | title = An empirical comparison of supervised learning algorithms | conference = Proc. 23rd International Conference on Machine Learning | year = 2006 | citeseerx = 10.1.1.122.5901 }}</ref>

An advantage of naive Bayes is that it only requires a small amount of training data to estimate the parameters necessary for classification.<ref>{{cite web |title=Why does Naive Bayes work better when the number of features >> sample size compared to more sophisticated ML algorithms? |url=https://stats.stackexchange.com/q/379383 |website=Cross Validated Stack Exchange |access-date=24 January 2023}}</ref>