From 49f5687bfe1cab561039c6e443be4c1a02a389b6 Mon Sep 17 00:00:00 2001
From: Jan Benda <jan.benda@uni-tuebingen.de>
Date: Mon, 17 Dec 2018 12:08:25 +0100
Subject: [PATCH] [regression] improved exercise

---
 regression/exercises/exercises01.tex | 28 ++++++++++++++++------------
 1 file changed, 16 insertions(+), 12 deletions(-)

diff --git a/regression/exercises/exercises01.tex b/regression/exercises/exercises01.tex
index 043ee93..a58e3da 100644
--- a/regression/exercises/exercises01.tex
+++ b/regression/exercises/exercises01.tex
@@ -58,18 +58,20 @@
 
 \begin{questions}
 
-  \question Implement the gradient descent for finding the parameters
-  of a straigth line \[ y = mx+b \] that we want to fit to the data in
-  the file \emph{lin\_regression.mat}.
-
-  In the lecture we already prepared most of the necessary functions:
-  1. the cost function (\code{lsqError()}), and 2. the gradient
-  (\code{lsqGradient()}). Read chapter 8 ``Optimization and gradient
-  descent'' in the script, in particular section 8.4 and exercise 8.4!
+  \question We want to fit the straigth line \[ y = mx+b \] to the
+  data in the file \emph{lin\_regression.mat}.
+
+  In the lecture we already prepared the cost function
+  (\code{lsqError()}), and the gradient (\code{lsqGradient()}) (read
+  chapter 8 ``Optimization and gradient descent'' in the script, in
+  particular section 8.4 and exercise 8.4!). With these functions in
+  place we here want to implement a gradient descend algorithm that
+  finds the minimum of the cost function and thus the slope and
+  intercept of the straigth line that minimizes the squared distance
+  to the data values.
 
   The algorithm for the descent towards the minimum of the cost
   function is as follows:
-  
   \begin{enumerate}
   \item Start with some arbitrary parameter values (intercept $b_0$
     and slope $m_0$, $\vec p_0 = (b_0, m_0)$ for the slope and the
@@ -106,9 +108,11 @@
       \lstinputlisting{../code/descentfit.m}
     \end{solution}
 
-    \part Find the position of the minimum of the cost function by
-    means of the \code{min()} function. Compare with the result of the
-    gradient descent method. Vary the value of $\epsilon$ and the
+    \part For checking the gradient descend method from (a) compare
+    its result for slope and intercept with the position of the
+    minimum of the cost function that you get when computing the cost
+    function for many values of the slope and intercept and then using
+    the \code{min()} function. Vary the value of $\epsilon$ and the
     minimum gradient. What are good values such that the gradient
     descent gets closest to the true minimum of the cost function?
     \begin{solution}