Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Theoretical Foundations of Equitability and the Maximal Information
  Coefficient   The maximal information coefficient (MIC) is a tool for finding the strongest
pairwise relationships in a data set with many variables (Reshef et al., 2011).
MIC is useful because it gives similar scores to equally noisy relationships of
different types. This property, called {\em equitability}, is important for
analyzing high-dimensional data sets.
  Here we formalize the theory behind both equitability and MIC in the language
of estimation theory. This formalization has a number of advantages. First, it
allows us to show that equitability is a generalization of power against
statistical independence. Second, it allows us to compute and discuss the
population value of MIC, which we call MIC_*. In doing so we generalize and
strengthen the mathematical results proven in Reshef et al. (2011) and clarify
the relationship between MIC and mutual information. Introducing MIC_* also
enables us to reason about the properties of MIC more abstractly: for instance,
we show that MIC_* is continuous and that there is a sense in which it is a
canonical "smoothing" of mutual information. We also prove an alternate,
equivalent characterization of MIC_* that we use to state new estimators of it
as well as an algorithm for explicitly computing it when the joint probability
density function of a pair of random variables is known. Our hope is that this
paper provides a richer theoretical foundation for MIC and equitability going
forward.
  This paper will be accompanied by a forthcoming companion paper that performs
extensive empirical analysis and comparison to other methods and discusses the
practical aspects of both equitability and the use of MIC and its related
statistics.

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The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
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The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: econ