What does it mean to say that two classifiers are independent? For example: http://www.tandfonline.com/doi/abs/10.1080/00031305.2013.778788
Is it simply that neither classifier uses the output of the other?
 A: This paper means independent in the statistical sense.
If classifiers $A$ and $B$ are independent, strictly speaking this means the predictions of $A$ give you no information about the predictions of $B$. However, this isn't a very useful idea: if both $A$ and $B$ have an accuracy of 0.6, say, and $A$ predicts $X$ is positive, then $X$ is more likely to be positive, which probably makes $B$ is more likely to predict that $X$ is positive!
As noted in the abstract you linked to, a more useful idea is that of independent errors--$A$ and $B$ have independent errors if their correctness or incorrectness on a given datum are not related. That is, if classifiers $A$ and $B$ have independent errors, and $A$ classifies instance $X$ correctly (whether as positive or negative), then this would tell you nothing about how likely $B$ is to classify $X$ correctly.
This is a desirable condition because it gives you some guarantees about ensembling $A$ and $B$ together. If you don't have independent errors--for instance, if $A$ and $B$ are exactly the same--then an ensemble of $A$ and $B$ might not be any better than $A$ or $B$ individually.
In practice, I think "independent classifiers" and "classifiers with independent errors" are sometimes conflated, so it's better not to be pedantic about it and try to understand what is meant from context.
