Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $f$-divergence and Loss Functions in ROC Curve   Given two data distributions and a test score function, the Receiver
Operating Characteristic (ROC) curve shows how well such a score separates two
distributions. However, can the ROC curve be used as a measure of discrepancy
between two distributions? This paper shows that when the data likelihood ratio
is used as the test score, the arc length of the ROC curve gives rise to a
novel $f$-divergence measuring the differences between two data distributions.
Approximating this arc length using a variational objective and empirical
samples leads to empirical risk minimization with previously unknown loss
functions. We provide a Lagrangian dual objective and introduce kernel models
into the estimation problem. We study the non-parametric convergence rate of
this estimator and show under mild smoothness conditions of the real arctangent
density ratio function, the rate of convergence is $O_p(n^{-\beta/4})$ ($\beta
\in (0,1]$ depends on the smoothness).

19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat