# Does 'Conditional Independence' means there should be no multicollinearity among features?

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?

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 $$1$$.
• @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 $Z$. – guy Sep 25 '18 at 15:36