Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proper likelihood ratio based ROC curves for general binary
  classification problems   Everybody writes that ROC curves, a very common tool in binary classification
problems, should be optimal, and in particular concave, non-decreasing and
above the 45-degree line. Everybody uses ROC curves, theoretical and especially
empirical, which are not so. This work is an attempt to correct this
schizophrenic behavior. Optimality stems from the Neyman-Pearson lemma, which
prescribes using likelihood-ratio based ROC curves. Starting from there, we
give the most general definition of a likelihood-ratio based classification
procedure, which encompasses finite, continuous and even more complex data
types. We point out a strict relationship with a general notion of
concentration of two probability measures. We give some nontrivial examples of
situations with non-monotone and non-continuous likelihood ratios. Finally, we
propose the ROC curve of a likelihood ratio based Gaussian kernel flexible
Bayes classifier as a proper default alternative to the usual empirical ROC
curve.

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The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
1
The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
2
The categories of this paper are: math