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I came across this paper about Naive Bayes that states

[Naive Bayes] is based on another common simplifying assumption: the values of numeric attributes are normally distributed within each class.

Is that true? Does Naive Bayes require that you assume continuous predictors are normal?

From this answer and my experience, I thought that you can use any distribution to describe your predictors, normal or otherwise. Am I missing something? Is the paper just badly worded, e.g. it should say "is commonly based on a normality assumption" instead of "is based on a normality assumption?"

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R Greg Stacey
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1 Answers1

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On its own, Naive Bayes does not assume the normal distribution. The heart of Naive Bayes is the heroic conditional independence assumption: $$P(x \mid X, C) = P(x \mid C)$$

Gaussian Naive Bayes assumes the normal distribution...

Matthew Gunn
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  • Is the paper badly worded / incorrect then? Do they just mean "Naive Bayes often assumes normality?" – R Greg Stacey May 31 '16 at 23:06
  • @Qroid Without reading anything (so I could be wrong), my guess is that they mean Gaussian Naive Bayes. Often times you need to read text reasonably rather than explicitly. – Matthew Gunn May 31 '16 at 23:09
  • Thanks. Didn't mean to nit pick. Just wondered if I understood correctly. – R Greg Stacey May 31 '16 at 23:42
  • It perform well in case of categorical input variables compared to numerical variable(s). For numerical variable, normal distribution is assumed (bell curve, which is a strong assumption). – MUK Jun 01 '21 at 07:53