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While I was going through the question How to interpret classification report of scikit-learn? with the following metrics -

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I saw following claim (in the accepted answer) -

you cannot compare the precision and the recall over two classes. This only means you're classifier is better to find class 0 over class 1.

I am not able to understand this statement. Shouldn't, in theory atleast, we be striving to get as high score as possible for both the classes separately? Also, this example is for a balanced class problem. What about imbalanced classes? I am assuming that we have a single binary classifier that is estimating P(Y=1|X) only. Could you please help? Thanks

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