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I am looking at how naive Bayes works and I see that it goes over all the classes and finds the probability that maximizes: $\log(\operatorname{Pr}[Y=y]) + \sum_{i=1}^d \log(\operatorname{Pr}[X_i=x_i|Y=y])$ So it looks like the probability for each feature is calculated separately.

So, my question is, is it possible that the distribution for each feature will be different? (For example $x_1\sim N(0,1)$ and $x_2\sim\mbox{Laplace}(\mu, b) $?

Davide Giraudo
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Lee
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  • I do not see any problems with 2 distribution, even non-parametric. – German Demidov Jan 21 '16 at 14:14
  • So the only constaint is that the distributions will be independent? – Lee Jan 21 '16 at 14:16
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    Yes, and the calculations can become more complicated for your case. Especially training of Bayes classifier. I guess you will have to code your own classifier for particular distributions. – German Demidov Jan 21 '16 at 14:21
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    [here](http://stats.stackexchange.com/questions/33185/difference-between-naive-bayes-multinomial-naive-bayes) is a piece of useful information (first answer) – German Demidov Jan 21 '16 at 14:28

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