an.tsouchlos/ba-thesis
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases 1 Wiki Activity

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

Browse Source
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
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

18
latex/presentations/midterm/sections/decoding_algorithms.tex
View File

@ -9,16 +9,21 @@
\begin{frame}[t] \begin{frame}[t]
\frametitle{Proximal Decoding: General Idea \cite{proximal_paper}} \frametitle{Proximal Decoding: General Idea \cite{proximal_paper}}
\vspace*{-0.3cm}
\begin{itemize} \begin{itemize}
\item MAP rule: \item MAP rule:
\begin{align*} \begin{align*}
\hat{\boldsymbol{x}} \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{Y}}\left( \boldsymbol{y} | \boldsymbol{x} \right)
f_{\boldsymbol{X}}\left( \boldsymbol{x} \right) f_{\boldsymbol{X}}\left( \boldsymbol{x} \right)\\
= \argmax_{x\in\mathbb{R}^n} &= \argmax_{x\in\mathbb{R}^n}
e^{-L\left( \boldsymbol{y} | \boldsymbol{x}\right)} 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*} \end{align*}
\item Approximation of prior PDF: \item Approximation of prior PDF:
\begin{align*} \begin{align*}
@ -64,10 +69,7 @@
\begin{align*} \begin{align*}
f\left( \boldsymbol{x} \right) f\left( \boldsymbol{x} \right)
= L\left( \boldsymbol{y} | \boldsymbol{x} \right) = L\left( \boldsymbol{y} | \boldsymbol{x} \right)
+ \gamma h\left( \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)
\end{align*} \end{align*}
\note{Notational difference between $f$ and $f_X$ or $f_Y$} \note{Notational difference between $f$ and $f_X$ or $f_Y$}
\item Proximal operator \cite{proximal_algorithms}: \item Proximal operator \cite{proximal_algorithms}:

2
latex/presentations/midterm/sections/forthcoming_examination.tex
View File

@ -7,7 +7,7 @@
\label{sub:Forth Exam LP Decoding} \label{sub:Forth Exam LP Decoding}
\begin{frame}[t] \begin{frame}[t]
\frametitle{Forthcoming Examinations} \frametitle{Forthcoming Analysis}
\begin{itemize} \begin{itemize}
\item Test ADMM (Alternating Direction Method of Multipliers) \item Test ADMM (Alternating Direction Method of Multipliers)