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[regression] improved exercise

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Jan Benda 2018-12-17 12:08:25 +01:00
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regression/exercises/exercises01.tex
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@ -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}