Pac-Bayesian supervised classification; the thermodynamics of statistical learning

Pac-Bayesian supervised classification; the thermodynamics of statistical learning.

Catoni, Olivier.

Inst./Mathematical Statistics

2007

163 pages

$108.00

Paperback

Lecture notes-monograph series; v.56

Q325

Caroni (probability, U. Paris 6) describes adaptive supervised classifications as analyzed by tools borrowed from statistical mechanics and information theory as proposed and developed by McAllester and Vapnik. He shows how to get local measures f the complexity of the classification model involving the relative entropy of posterior distributions as it relates to Gibbs posterior measures, progressing in complexity. Therefore he begins with inductive PAC-Bayesian learning, covering basic inequality, non local bounds, local bounds and relative bounds, then compares posterior distributions to Gibbs priors, covering bounds relative to a Gibbs distribution, work with two posteriors and two local prior distributions, and two-step localization. In issues of transductive PAC-Bayesian learning he covers basic inequalities, Vapnik bounds for transductive or inductive classifications, Gaussian approximations in Vapnik bounds, and support vector machines, including how to build them.

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