Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pac-Bayesian Supervised Classification: The Thermodynamics of
  Statistical Learning   This monograph deals with adaptive supervised classification, using tools
borrowed from statistical mechanics and information theory, stemming from the
PACBayesian approach pioneered by David McAllester and applied to a conception
of statistical learning theory forged by Vladimir Vapnik. Using convex analysis
on the set of posterior probability measures, we show how to get local measures
of the complexity of the classification model involving the relative entropy of
posterior distributions with respect to Gibbs posterior measures. We then
discuss relative bounds, comparing the generalization error of two
classification rules, showing how the margin assumption of Mammen and Tsybakov
can be replaced with some empirical measure of the covariance structure of the
classification model.We show how to associate to any posterior distribution an
effective temperature relating it to the Gibbs prior distribution with the same
level of expected error rate, and how to estimate this effective temperature
from data, resulting in an estimator whose expected error rate converges
according to the best possible power of the sample size adaptively under any
margin and parametric complexity assumptions. We describe and study an
alternative selection scheme based on relative bounds between estimators, and
present a two step localization technique which can handle the selection of a
parametric model from a family of those. We show how to extend systematically
all the results obtained in the inductive setting to transductive learning, and
use this to improve Vapnik's generalization bounds, extending them to the case
when the sample is made of independent non-identically distributed pairs of
patterns and labels. Finally we review briefly the construction of Support
Vector Machines and show how to derive generalization bounds for them,
measuring the complexity either through the number of support vectors or
through the value of the transductive or inductive margin.

8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex