diff --git a/is/ub9/is9.pdf b/is/ub9/is9.pdf new file mode 100644 index 0000000..727b3ac --- /dev/null +++ b/is/ub9/is9.pdf Binary files differ diff --git a/is/ub9/is9.tex b/is/ub9/is9.tex new file mode 100644 index 0000000..97125be --- /dev/null +++ b/is/ub9/is9.tex @@ -0,0 +1,96 @@ +\documentclass[a4paper,12pt]{scrartcl} +\usepackage[ngerman]{babel} +\usepackage{graphicx} %BIlder einbinden +\usepackage{amsmath} %erweiterte Mathe-Zeichen +\usepackage{amsfonts} %weitere fonts +\usepackage[utf8]{inputenc} %Umlaute & Co +\usepackage{hyperref} %Links +\usepackage{ifthen} %ifthenelse +\usepackage{enumerate} +\usepackage{listings} +\lstset{language=Python} + +\usepackage{algpseudocode} %Pseudocode +\usepackage{dsfont} % schöne Zahlenräumezeichen +\usepackage{amssymb, amsthm} %noch stärker erweiterte Mathe-Zeichen +\usepackage{tikz} %TikZ ist kein Zeichenprogramm +\usetikzlibrary{trees,automata,arrows,shapes} + +\pagestyle{empty} + + +\topmargin-50pt + +\newcounter{aufgabe} +\def\tand{&} + +\newcommand{\makeTableLine}[2][0]{% + \setcounter{aufgabe}{1}% + \whiledo{\value{aufgabe} < #1}% + {% + #2\tand\stepcounter{aufgabe}% + } +} + +\newcommand{\aufgTable}[1]{ + \def\spalten{\numexpr #1 + 1 \relax} + \begin{tabular}{|*{\spalten}{p{1cm}|}} + \makeTableLine[\spalten]{A\theaufgabe}$\Sigma$~~\\ \hline + \rule{0pt}{15pt}\makeTableLine[\spalten]{}\\ + \end{tabular} +} + +\def\header#1#2#3#4#5#6#7{\pagestyle{empty} +\begin{minipage}[t]{0.47\textwidth} +\begin{flushleft} +{\bf #4}\\ +#5 +\end{flushleft} +\end{minipage} +\begin{minipage}[t]{0.5\textwidth} +\begin{flushright} +#6 \vspace{0.5cm}\\ +% Number of Columns Definition of Columns second empty line +% \begin{tabular}{|*{5}{C{1cm}|}}\hline A1&A2&A3&A4&$\Sigma$\\\hline&&&&\\\hline\end{tabular}\\\vspace*{0.1cm} +\aufgTable{#7} +\end{flushright} +\end{minipage} +\vspace{1cm} +\begin{center} +{\Large\bf Sheet #1} + +{(Hand in #3)} +\end{center} +} + + + +%counts the exercisenumber +\newcounter{n} + +%Kommando für Aufgaben +%\Aufgabe{AufgTitel}{Punktezahl} +\newcommand{\Aufgabe}[2]{\stepcounter{n} + \textbf{Exercise \arabic{n}: #1} (#2 Points)} + + +\begin{document} + %\header{BlattNr}{Tutor}{Abgabedatum}{Vorlesungsname}{Namen}{Semester}{Anzahl Aufgaben} + \header{9}{}{2015-07-09}{Intelligent Systems I}{\textit{Maximus Mutschler}\\ \textit{Jan-Peter Hohloch} + }{SS 15}{2} + \vspace{1cm} + \Aufgabe{Independence}{50}\\ + \includegraphics[width=0.49\textwidth]{regression.png} + \includegraphics[width=0.49\textwidth]{residuals.png}\\ + %TODO + TODO: why are they not independent + \Aufgabe{Kernels}{50} + \begin{enumerate} + \item $k(x_1,x_2)=C=\sqrt{C}^2\cdot k'(x_1,x_2)$, where $k'(x_1,x_2)=1$ which is clearly positive semidefinite. + \item is p.d. according to the lecture, because it's a polynomial kernel + \item TODO: don't see why not in the hint-case + \item As 2. is a kernel, this is too with $\alpha=\sqrt{5}$ + \item As $k_1(x_1,x_2)=x_1^Tx_2$ and $k_2(x_1,x_2)=1$ are kernels, their sum is too. Now we multiply the sum of this kernels with itself and get another kernel. + \end{enumerate} +\end{document} +