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Edit: Generalization error vs. marginal likelihood (#10)
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The paragraph renamed from Bayes free energy vs. generalization loss
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yousuketakada committed Apr 8, 2018
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Expand Up @@ -1994,11 +1994,12 @@ \subsubsection*{#1}
Bayesian model comparison to work;
see the discussion around (3.73).

\parhead{Bayes free energy vs.\ generalization loss}
\parhead{Generalization error vs.\ marginal likelihood}
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),
(i)~the \emph{generalization error},
which can be estimated by cross-validation (Section~3.2), and
(ii)~the \emph{marginal likelihood},
which is used in the Bayesian model comparison framework (Section~3.4),
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.
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