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  \textbf{\textsc{STANFORD UNIVERSITY}}\\[5pt]
  \textbf{\textsc{DEPARTMENT OF STATISTICS}}\\[5pt]
  \Large{\textbf\textsc{{DEPARTMENTAL SEMINAR}}}
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\begin{center}
  4:15 p.m., Tuesday, March 14, 2006\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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\begin{center}
  \textsl{Lutz Duembgen}\\
University of Berne
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  \textbf{P-Values for Classification}
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\noindent



Abstract: Let $(X,Y)$ be a complete observation consisting of a feature
vector $X$ and a class label $Y \in \{1,2,\ldots,K\}$. Classification
means to predict the unobserved class label $Y$ from the observed
feature vector $X$. The joint distribution of $(X,Y)$ is typically
unknown and estimated from certain training data. We propose to replace
classifiers (i.e. point predictors) or the (estimated) posterior
distribution $L(Y \vert X)$ with a tupel of p-values for the $K$
potential class memberships. After a brief discussion of the potential
benefits of this approach, we extend the classical theory of optimal
classifiers to optimal p-values. Thereafter we discuss the impact of
estimating the joint distribution from training data and describe a
general method based on permutation tests. Some theoretical results and
numerical examples show the method's potential.
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