課程名稱︰機器學習
課程性質︰電機系選修
課程教師︰吳沛遠
開課學院：電機資訊學院
開課系所︰電機工程學系
考試日期（年月日）︰2018/12/28
試題 :
The paper consists of 9 questions. Total 105 points + 10 bonus points. In this
exam we denote
● Sigmoid function: $\sigma(z) = \frac1{1+e^{-z}}$. You may apply approximate
$\sigma(z) \approx \begin{cases}0,&\text{if }z\le-10,\\1,&\text{if }z\ge10.
\end{cases}$
● Sign function: $\operatorname{sgn}(z) = \begin{cases}1,&\text{if }z>0,\\0,
&\text{if }z=0,\\-1,&\text{if }z<0.\end{cases}$
● Unless otherwise specified, all log refer to natural log, i.e., $\log_e$.
Problem 1: (20 pts) Multiple Selection (多選題有倒扣，最多倒扣至本大題零分)
Please answer the following multiple selection questions. Wrong selections will
result in inverted scores. No derivation required.
(1) Suppose you are using a hard margin linear SVM classifier on 2 class clas-
sification problem. Now you have been given the following data in which
some points are dashed-circled that are representing support vectors.
https://i.imgur.com/0YlXylk.png
\begin{tikzpicture}
\def\ok{
-2.3/2.6, -1.8/1.9, -1.7/1, -1.6/2.4, -1.3/3.2,
-1.2/1.8, -1/3.9, -.9/2.5, -.7/1.4, -.5/2.2,
-.5/3.4, -.4/2.9, .2/2.6, .2/3.1, .7/3.3
}
\def\ng{
.7/0, .8/.6, 1.1/-.3, 1.2/.8, 1.3/.3,
1.6/1.1, 1.8/-.1, 1.9/.7, 2/1.7, 2.4/1.2,
2.4/2.1, 2.5/.6, 2.7/1.7, 3.1/2.2
}
\foreach \x/\y in \ok{
\draw (\x, \y) circle(1pt);
}
\foreach \x/\y in \ng{
\filldraw (\x, \y) circle(1pt);
}
\def\sx{{0, .2, 1.4}}
\def\sy{{1.7, .5, 1.8}}
\draw (\sx[0], \sy[0]) circle(1pt);
\draw[densely dotted] (\sx[0], \sy[0]) circle(2pt);
\foreach \i in {1, 2}{
\filldraw (\sx[\i], \sy[\i]) circle(1pt);
\draw[densely dotted] (\sx[\i], \sy[\i]) circle(2pt);
}
\foreach \i in {0, 1, 2}{
\draw[very thin, -stealth] (1.3, 3)