From 25d7a9eac4805671adf12783da4ef575ff88b4fb Mon Sep 17 00:00:00 2001 From: Yousuke Takada Date: Sun, 8 Apr 2018 11:42:38 +0900 Subject: [PATCH] Edit: A Bayesian model that exhibits overfitting (#10) --- prml_errata.tex | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/prml_errata.tex b/prml_errata.tex index cb52c8e..062ff87 100644 --- a/prml_errata.tex +++ b/prml_errata.tex @@ -1971,12 +1971,12 @@ \subsubsection*{#1} whereas the precision~$\alpha$ of the parameters~$\mathbf{w}$ in the prior~(3.52) is very small (i.e., the conditional distribution of $t$ given $\mathbf{w}$ is narrow whereas the prior over $\mathbf{w}$ is broad), leading to insufficient \emph{regularization} -(see also Section~3.1.4). -Then, the posterior~$p(\mathbf{w}|\bm{\mathsf{t}})$ given the data set~$\bm{\mathsf{t}}$ is +(see Section~3.1.4). +Then, the posterior~$p(\mathbf{w}|\bm{\mathsf{t}})$ given the data set~$\bm{\mathsf{t}}$ will be sharply peaked around the maximum likelihood estimate~$\mathbf{w}_{\text{ML}}$ and -the predictive~$p(t|\bm{\mathsf{t}})$ is also sharply peaked -(well approximated by the likelihood conditioned on $\mathbf{w}_{\text{ML}}$) -so that the assumed model reduces to the least squares method, +the predictive~$p(t|\bm{\mathsf{t}})$ be also sharply peaked +(well approximated by the likelihood conditioned on $\mathbf{w}_{\text{ML}}$). +Stated differently, the assumed model reduces to the least squares method, which is known to suffer from overfitting (see Section~1.1). Of course, we can extend the model by incorporating hyperpriors over $\beta$ and $\alpha$,