I was reading the Naive Bayes article on Wikipedia and I read that, In Naive Bayes, the naive assumption that Naive Bayes make is "each feature is conditionally independent of every other feature, given the category Ck". So, I was wondering if 'Conditional Independence' means there should be no multicollinearity among features?


1 Answer 1


No, it does not imply lack of multicolineaity. Suppose $X$ and $Y$ are normal with variance 0.001, and have mean $\mu = 100$ if $Z = 1$ and mean $\mu = -100$ if $Z = 0$, but are conditionally independent given $Z$. There is still extreme multicolineairty here, with the correlation being very close to $1$.

  • $\begingroup$ So, What could be an intuitive explanation of conditional independence in Naive Bayes? $\endgroup$ Sep 25, 2018 at 14:27
  • $\begingroup$ @AkashDubey I fail to see how multicollinearity has anything to do with conditional independence or Naive Bayes here. Are you running into this problem with a data analysis? As an example, two factors can have 0 prevalence but be conditionally independent, as such both terms are nominally multicollinear, but not necessarily dependent. $\endgroup$
    – AdamO
    Sep 25, 2018 at 15:03
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    $\begingroup$ @AkashDubey conditional independence states that if you knew $Z$ in this example, then they are independent. This implies that at every fixed level of $Z$ in the above example, you will not have multicolinearity. But you can still have multicolinearity if you ignore $Z$. $\endgroup$
    – guy
    Sep 25, 2018 at 15:36

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