People always said that naive Bayes is a linear model. I am not able to understand why, so can anybody explain?
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$\begingroup$ Perhaps you could give a reference to where it's called linear and also say why this does not make sense to you? $\endgroup$– WayneCommented Jun 28, 2013 at 14:43
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$\begingroup$ This question contains the proof for a Multinomial Naive Bayes model. $\endgroup$– Bharat KhatriCommented Feb 8, 2015 at 8:19
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I don't see how Naive Bayes is a linear model. This gives one possible definition. In general, I would say a linear model would involve a linear combination of the parameters or of some transformation of the parameters.
Naive Bayes multiplies the probabilities from the different variables and they are also not really weighted in the standard sense. However, if you take the logarithm this will become addition, so it is possible that given some type of conditional probability distribution (CPD) you could get something that looks like a linear model. I don't think this is true for every CPD though (but I may be wrong).
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$\begingroup$ If the predicted distribution is a noncurved exponential family, the naive Bayes prediction is a linear combination of natural parameters of predictive distributions. Is this what you're referring to? $\endgroup$– Neil GCommented Jun 28, 2013 at 19:22
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$\begingroup$ A linear model would involve a linear combination of the parameters or some transformation
of a linear combination of the parameters. $\endgroup$ Commented Feb 8, 2015 at 8:16