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Edit: Bayes free energy vs. generalization loss
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yousuketakada committed Apr 7, 2018
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Expand Up @@ -1994,12 +1994,14 @@ \subsubsection*{#1}
Bayesian model comparison to work;
see the discussion around (3.73).

Moreover, one should also be aware of a subtlety here, that is,
(i)~the \emph{generalization error}, which can be measured by cross-validation, and
(ii)~the \emph{model evidence} (or the \emph{marginal likelihood})
are closely related but different criteria,
although, in practice, a higher model evidence often tends to imply a lower generalization error
and vice versa.
\parhead{Bayes free energy vs.\ generalization loss}
Moreover, one should also be aware of a subtlety that
(i)~the \emph{marginal likelihood},
which is used in the Bayesian model comparison framework (see Section~3.4), and
(ii)~the \emph{generalization error}, which can be estimated by cross-validation (Section~3.2),
are closely related but different criteria for assessing model complexity,
although, in practice, a higher marginal likelihood often tends to imply
a lower generalization error and vice versa.
For more (advanced) discussions, see \citet{Watanabe:WAIC,Watanabe:WBIC}.

\erratum{Page~156}
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