Achieved information gain, the ideal-minus-remaining relative entropy, quantifies how much of an update to a belief state is actually correct and can be negative for misleading updates.
Signal Enhancement as Minimization of Relevant Information Loss
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abstract
We introduce the notion of relevant information loss for the purpose of casting the signal enhancement problem in information-theoretic terms. We show that many algorithms from machine learning can be reformulated using relevant information loss, which allows their application to the aforementioned problem. As a particular example we analyze principle component analysis for dimensionality reduction, discuss its optimality, and show that the relevant information loss can indeed vanish if the relevant information is concentrated on a lower-dimensional subspace of the input space.
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Quantifying imperfect cognition via achieved information gain
Achieved information gain, the ideal-minus-remaining relative entropy, quantifies how much of an update to a belief state is actually correct and can be negative for misleading updates.