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[regression] updated exercise

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Jan Benda 2018-12-11 16:04:53 +01:00
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regression/exercises/exercises01.tex
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@ -20,7 +20,7 @@
\else \else
\newcommand{\stitle}{} \newcommand{\stitle}{}
\fi \fi
\header{{\bfseries\large Exercise 11\stitle}}{{\bfseries\large Gradient descent}}{{\bfseries\large January 9th, 2018}} \header{{\bfseries\large Exercise 10\stitle}}{{\bfseries\large Gradient descent}}{{\bfseries\large December 17th, 2018}}
\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: \firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email:
jan.grewe@uni-tuebingen.de} jan.grewe@uni-tuebingen.de}
\runningfooter{}{\thepage}{} \runningfooter{}{\thepage}{}
@ -59,12 +59,11 @@
\begin{questions} \begin{questions}
\question Implement the gradient descent for finding the parameters \question Implement the gradient descent for finding the parameters
of a straigth line that we want to fit to the data in the file of a straigth line \[ y = mx+b \] that we want to fit to the data in
\emph{lin\_regression.mat}. the file \emph{lin\_regression.mat}.
In the lecture we already prepared most of the necessary functions: In the lecture we already prepared most of the necessary functions:
1. the error function (\code{meanSquareError()}), 2. the cost 1. the cost function (\code{lsqError()}), and 2. the gradient
function (\code{lsqError()}), and 3. the gradient
(\code{lsqGradient()}). Read chapter 8 ``Optimization and gradient (\code{lsqGradient()}). Read chapter 8 ``Optimization and gradient
descent'' in the script, in particular section 8.4 and exercise 8.4! descent'' in the script, in particular section 8.4 and exercise 8.4!
@ -72,8 +71,9 @@
function is as follows: function is as follows:
\begin{enumerate} \begin{enumerate}
\item Start with some arbitrary parameter values $\vec p_0 = (m_0, b_0)$ \item Start with some arbitrary parameter values (intercept $b_0$
for the slope and the intercept of the straight line. and slope $m_0$, $\vec p_0 = (b_0, m_0)$ for the slope and the
intercept of the straight line.
\item \label{computegradient} Compute the gradient of the cost function \item \label{computegradient} Compute the gradient of the cost function
at the current values of the parameters $\vec p_i$. at the current values of the parameters $\vec p_i$.
\item If the magnitude (length) of the gradient is smaller than some \item If the magnitude (length) of the gradient is smaller than some