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We propose a framework to analyze and quantify the bias in adaptive data analysis. It generalizes that proposed by Russo and Zou'15, applying to measurements whose moment generating function exists, measurements with a finite p-norm, and measurements in general Orlicz spaces. We introduce a new class of dependence measures which retain key properties of mutual information while more effectively quantifying...
The mutual information between two jointly distributed random variables $X$ and $Y$ is a functional of the joint distribution $P_{XY}$ , which is sometimes difficult to handle or estimate. A coarser description of the statistical behavior of $(X,Y)$ is given by the marginal distributions $P_{X}, P_{Y}$ and the adjacency relation induced by the joint distribution, where $x$ and $y$ are...
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