Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Connecting population-level AUC and latent scale-invariant $R^2$ via
  Semiparametric Gaussian Copula and rank correlations   Area Under the Curve (AUC) is arguably the most popular measure of
classification accuracy. We use a semiparametric framework to introduce a
latent scale-invariant $R^2$, a novel measure of variation explained for an
observed binary outcome and an observed continuous predictor, and then directly
link the latent $R^2$ to AUC. This enables a mutually consistent simultaneous
use of AUC as a measure of classification accuracy and the latent $R^2$ as a
scale-invariant measure of explained variation. Specifically, we employ
Semiparametric Gaussian Copula (SGC) to model a joint dependence between
observed binary outcome and observed continuous predictor via the correlation
of latent standard normal random variables. Under SGC, we show how, both
population-level AUC and latent scale-invariant $R^2$, defined as a squared
latent correlation, can be estimated using any of the four rank statistics
calculated on binary-continuous pairs: Wilcoxon rank-sum, Kendall's Tau,
Spearman's Rho, and Quadrant rank correlations. We then focus on three
implications and applications: i) we explicitly show that under SGC, the
population-level AUC and the population-level latent $R^2$ are related via a
monotone function that depends on the population-level prevalence rate, ii) we
propose Quadrant rank correlation as a robust semiparametric version of AUC;
iii) we demonstrate how, under complex-survey designs, Wilcoxon rank sum
statistics and Spearman and Quadrant rank correlations provide asymptotically
consistent estimators of the population-level AUC using only single-participant
survey weights. We illustrate these applications using binary outcome of
five-year mortality and continuous predictors including Albumin, Systolic Blood
Pressure, and accelerometry-derived measures of total volume of physical
activity collected in 2003-2006 National Health and Nutrition Examination
Survey (NHANES) cohorts.

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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: math
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: dg-ga