Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moments and Root-Mean-Square Error of the Bayesian MMSE Estimator of
  Classification Error in the Gaussian Model   The most important aspect of any classifier is its error rate, because this
quantifies its predictive capacity. Thus, the accuracy of error estimation is
critical. Error estimation is problematic in small-sample classifier design
because the error must be estimated using the same data from which the
classifier has been designed. Use of prior knowledge, in the form of a prior
distribution on an uncertainty class of feature-label distributions to which
the true, but unknown, feature-distribution belongs, can facilitate accurate
error estimation (in the mean-square sense) in circumstances where accurate
completely model-free error estimation is impossible. This paper provides
analytic asymptotically exact finite-sample approximations for various
performance metrics of the resulting Bayesian Minimum Mean-Square-Error (MMSE)
error estimator in the case of linear discriminant analysis (LDA) in the
multivariate Gaussian model. These performance metrics include the first,
second, and cross moments of the Bayesian MMSE error estimator with the true
error of LDA, and therefore, the Root-Mean-Square (RMS) error of the estimator.
We lay down the theoretical groundwork for Kolmogorov double-asymptotics in a
Bayesian setting, which enables us to derive asymptotic expressions of the
desired performance metrics. From these we produce analytic finite-sample
approximations and demonstrate their accuracy via numerical examples. Various
examples illustrate the behavior of these approximations and their use in
determining the necessary sample size to achieve a desired RMS. The
Supplementary Material contains derivations for some equations and added
figures.

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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: cs