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Fixed title; Moved neg. log likelihood def. to other slide

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This commit is contained in:
Andreas Tsouchlos 2023-01-27 02:43:54 +01:00
parent 052bb57834
commit a61a7f5b4c
2 changed files with 11 additions and 9 deletions
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18
latex/presentations/midterm/sections/decoding_algorithms.tex
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@ -9,16 +9,21 @@
\begin{frame}[t]
\frametitle{Proximal Decoding: General Idea \cite{proximal_paper}}
\vspace*{-0.3cm}
\begin{itemize}
\item MAP rule:
\begin{align*}
\hat{\boldsymbol{x}}
= \argmax_{x\in\mathbb{R}^n}
&= \argmax_{x\in\mathbb{R}^n}
f_{\boldsymbol{Y}}\left( \boldsymbol{y} | \boldsymbol{x} \right)
f_{\boldsymbol{X}}\left( \boldsymbol{x} \right)
= \argmax_{x\in\mathbb{R}^n}
f_{\boldsymbol{X}}\left( \boldsymbol{x} \right)\\
&= \argmax_{x\in\mathbb{R}^n}
e^{-L\left( \boldsymbol{y} | \boldsymbol{x}\right)}
f_{\boldsymbol{X}}\left( \boldsymbol{x} \right)
f_{\boldsymbol{X}}\left( \boldsymbol{x} \right),
\hspace{5mm} L\left( \boldsymbol{y} | \boldsymbol{x} \right)
= - \ln\left( f_{\boldsymbol{Y}}
\left( \boldsymbol{y} | \boldsymbol{x} \right) \right)
\end{align*}
\item Approximation of prior PDF:
\begin{align*}
@ -64,10 +69,7 @@
\begin{align*}
f\left( \boldsymbol{x} \right)
= L\left( \boldsymbol{y} | \boldsymbol{x} \right)
+ \gamma h\left( \boldsymbol{x} \right),
\hspace{5mm} L\left( \boldsymbol{y} | \boldsymbol{x} \right)
= - \ln\left( f_{\boldsymbol{Y}}
\left( \boldsymbol{y} | \boldsymbol{x} \right) \right)
+ \gamma h\left( \boldsymbol{x} \right)
\end{align*}
\note{Notational difference between $f$ and $f_X$ or $f_Y$}
\item Proximal operator \cite{proximal_algorithms}:

2
latex/presentations/midterm/sections/forthcoming_examination.tex
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@ -7,7 +7,7 @@
\label{sub:Forth Exam LP Decoding}
\begin{frame}[t]
\frametitle{Forthcoming Examinations}
\frametitle{Forthcoming Analysis}
\begin{itemize}
\item Test ADMM (Alternating Direction Method of Multipliers)