This commit is contained in:
Morten Hjorth-Jensen
2025-09-14 20:37:49 +02:00
parent c1a07a1b9f
commit fcbe09a20d
7 changed files with 135 additions and 135 deletions
+2 -2
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@@ -293,13 +293,13 @@ We could now define a new cost function to minimize, namely the negative logarit
!bt
\[
C(\bm{\theta}=-\log{\prod_{i=0}^{n-1}p(y_i,\bm{X}\vert\bm{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\bm{X}\vert\bm{\theta})},
C(\bm{\theta})=-\log{\prod_{i=0}^{n-1}p(y_i,\bm{X}\vert\bm{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\bm{X}\vert\bm{\theta})},
\]
!et
which becomes
!bt
\[
C(\bm{\theta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\bm{y}-\bm{X}\bm{\theta})\vert\vert_2^2}{2\sigma^2}.
C(\bm{\theta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\bm{y}-\bm{X}\bm{\theta})\vert\vert_2^2}{2\sigma^2}.
\]
!et