From a61a7f5b4cfe52a0ed8bc8195f15362ff526b177 Mon Sep 17 00:00:00 2001
From: Andreas Tsouchlos <an.tsouchlos@gmail.com>
Date: Fri, 27 Jan 2023 02:43:54 +0100
Subject: [PATCH] Fixed title; Moved neg. log likelihood def. to other slide

---
 .../midterm/sections/decoding_algorithms.tex   | 18 ++++++++++--------
 .../sections/forthcoming_examination.tex       |  2 +-
 2 files changed, 11 insertions(+), 9 deletions(-)

diff --git a/latex/presentations/midterm/sections/decoding_algorithms.tex b/latex/presentations/midterm/sections/decoding_algorithms.tex
index b99d64c..9ca874a 100644
--- a/latex/presentations/midterm/sections/decoding_algorithms.tex
+++ b/latex/presentations/midterm/sections/decoding_algorithms.tex
@@ -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}:
diff --git a/latex/presentations/midterm/sections/forthcoming_examination.tex b/latex/presentations/midterm/sections/forthcoming_examination.tex
index 16db46a..d3889c7 100644
--- a/latex/presentations/midterm/sections/forthcoming_examination.tex
+++ b/latex/presentations/midterm/sections/forthcoming_examination.tex
@@ -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)