|
|
\documentclass[a4paper, 12pt, draft=true]{article}
|
|
|
|
|
|
%\usepackage[margin=1in]{geometry}
|
|
|
%\geometry{a4paper, left=30mm, right=40mm,top=25mm, bottom=20mm}
|
|
|
|
|
|
\usepackage[english]{babel}
|
|
|
\usepackage[utf8]{inputenc}
|
|
|
\usepackage[T1]{fontenc}
|
|
|
\usepackage{textcomp}
|
|
|
%\usepackage{libertine}
|
|
|
\usepackage{amsmath}
|
|
|
%\usepackage{amssymb}
|
|
|
\usepackage{amsthm}
|
|
|
\usepackage{amsfonts}
|
|
|
\usepackage{graphicx}
|
|
|
\usepackage{wrapfig}
|
|
|
\usepackage{enumerate}
|
|
|
\usepackage{sectsty}
|
|
|
\usepackage{setspace}
|
|
|
\usepackage{booktabs}
|
|
|
\usepackage[format=plain,
|
|
|
textfont=it]{caption}
|
|
|
%\usepackage{natbib} %[numbers]
|
|
|
\usepackage{multirow}
|
|
|
\usepackage{3parttable}
|
|
|
\usepackage{mathtools}
|
|
|
\usepackage{tabu}
|
|
|
\usepackage{makecell}
|
|
|
\usepackage{dsfont}
|
|
|
\usepackage{tikz}
|
|
|
\usepackage{nicefrac}
|
|
|
\usepackage{enumitem}
|
|
|
\usepackage[toc, page]{appendix}
|
|
|
\usepackage{todonotes}
|
|
|
\usepackage{lipsum}
|
|
|
\usepackage[ruled,vlined]{algorithm2e}
|
|
|
%\usepackage{showframe}
|
|
|
\usepackage[protrusion=true, expansion=true, kerning=true, letterspace
|
|
|
= 150]{microtype}
|
|
|
\usepackage{titlecaps}
|
|
|
\usepackage{afterpage}
|
|
|
\usepackage{xcolor}
|
|
|
\usepackage{chngcntr}
|
|
|
|
|
|
\captionsetup[sub]{justification=centering}
|
|
|
|
|
|
\usetikzlibrary{matrix,chains,positioning,decorations.pathreplacing,arrows}
|
|
|
\usetikzlibrary{positioning,calc,calligraphy}
|
|
|
\usetikzlibrary{calc, 3d}
|
|
|
|
|
|
\usepackage{pgfplots}
|
|
|
\usepgfplotslibrary{colorbrewer}
|
|
|
\usepackage{subcaption}
|
|
|
\usetikzlibrary{arrows,decorations.markings}
|
|
|
\pgfplotsset{compat = 1.16}
|
|
|
\usepackage[export]{adjustbox}
|
|
|
|
|
|
\definecolor{maroon}{cmyk}{0, 0.87, 0.68, 0.32}
|
|
|
\definecolor{halfgray}{gray}{0.55}
|
|
|
\definecolor{ipython_frame}{RGB}{207, 207, 207}
|
|
|
\definecolor{ipython_bg}{RGB}{247, 247, 247}
|
|
|
\definecolor{ipython_red}{RGB}{186, 33, 33}
|
|
|
\definecolor{ipython_green}{RGB}{0, 128, 0}
|
|
|
\definecolor{ipython_cyan}{RGB}{64, 128, 128}
|
|
|
\definecolor{ipython_purple}{RGB}{110, 64, 130}
|
|
|
|
|
|
\usepackage{listings}
|
|
|
\usepackage{float}
|
|
|
|
|
|
\newfloat{lstfloat}{htbp}{lop}
|
|
|
\floatname{lstfloat}{Listing}
|
|
|
\def\lstfloatautorefname{Listing}
|
|
|
|
|
|
\lstset{
|
|
|
breaklines=true,
|
|
|
%
|
|
|
extendedchars=true,
|
|
|
literate=
|
|
|
{á}{{\'a}}1 {é}{{\'e}}1 {í}{{\'i}}1 {ó}{{\'o}}1 {ú}{{\'u}}1
|
|
|
{Á}{{\'A}}1 {É}{{\'E}}1 {Í}{{\'I}}1 {Ó}{{\'O}}1 {Ú}{{\'U}}1
|
|
|
{à}{{\`a}}1 {è}{{\`e}}1 {ì}{{\`i}}1 {ò}{{\`o}}1 {ù}{{\`u}}1
|
|
|
{À}{{\`A}}1 {È}{{\'E}}1 {Ì}{{\`I}}1 {Ò}{{\`O}}1 {Ù}{{\`U}}1
|
|
|
{ä}{{\"a}}1 {ë}{{\"e}}1 {ï}{{\"i}}1 {ö}{{\"o}}1 {ü}{{\"u}}1
|
|
|
{Ä}{{\"A}}1 {Ë}{{\"E}}1 {Ï}{{\"I}}1 {Ö}{{\"O}}1 {Ü}{{\"U}}1
|
|
|
{â}{{\^a}}1 {ê}{{\^e}}1 {î}{{\^i}}1 {ô}{{\^o}}1 {û}{{\^u}}1
|
|
|
{Â}{{\^A}}1 {Ê}{{\^E}}1 {Î}{{\^I}}1 {Ô}{{\^O}}1 {Û}{{\^U}}1
|
|
|
{œ}{{\oe}}1 {Œ}{{\OE}}1 {æ}{{\ae}}1 {Æ}{{\AE}}1 {ß}{{\ss}}1
|
|
|
{ç}{{\c c}}1 {Ç}{{\c C}}1 {ø}{{\o}}1 {å}{{\r a}}1 {Å}{{\r A}}1
|
|
|
{€}{{\EUR}}1 {£}{{\pounds}}1
|
|
|
}
|
|
|
|
|
|
%%
|
|
|
%% Python definition (c) 1998 Michael Weber
|
|
|
%% Additional definitions (2013) Alexis Dimitriadis
|
|
|
%% modified by me (should not have empty lines)
|
|
|
%%
|
|
|
\lstdefinelanguage{iPython}{
|
|
|
morekeywords={access,and,break,class,continue,def,del,elif,else,except,exec,finally,for,from,global,if,import,
|
|
|
in,is,lambda,not,or,pass,print,raise,return,try,while},%
|
|
|
%
|
|
|
% Built-ins
|
|
|
morekeywords=[2]{abs,all,any,basestring,bin,bool,bytearray,callable,chr,classmethod,cmp,compile,complex,delattr,dict,dir,divmod,enumerate,eval,execfile,file,filter,float,format,frozenset,getattr,globals,hasattr,hash,help,hex,id,input,int,isinstance,issubclass,iter,len,list,locals,long,map,max,memoryview,min,next,object,oct,open,ord,pow,property,range,raw_input,reduce,reload,repr,reversed,round,set,setattr,slice,sorted,staticmethod,str,sum,super,tuple,type,unichr,unicode,vars,xrange,zip,apply,buffer,coerce,intern,val},%
|
|
|
%
|
|
|
sensitive=true,%
|
|
|
morecomment=[l]\#,%
|
|
|
morestring=[b]',%
|
|
|
morestring=[b]",%
|
|
|
%
|
|
|
morestring=[s]{'''}{'''},% used for documentation text (mulitiline strings)
|
|
|
morestring=[s]{"""}{"""},% added by Philipp Matthias Hahn
|
|
|
%
|
|
|
morestring=[s]{r'}{'},% `raw' strings
|
|
|
morestring=[s]{r"}{"},%
|
|
|
morestring=[s]{r'''}{'''},%
|
|
|
morestring=[s]{r"""}{"""},%
|
|
|
morestring=[s]{u'}{'},% unicode strings
|
|
|
morestring=[s]{u"}{"},%
|
|
|
morestring=[s]{u'''}{'''},%
|
|
|
morestring=[s]{u"""}{"""},%
|
|
|
%
|
|
|
% {replace}{replacement}{lenght of replace}
|
|
|
% *{-}{-}{1} will not replace in comments and so on
|
|
|
literate=
|
|
|
{á}{{\'a}}1 {é}{{\'e}}1 {í}{{\'i}}1 {ó}{{\'o}}1 {ú}{{\'u}}1
|
|
|
{Á}{{\'A}}1 {É}{{\'E}}1 {Í}{{\'I}}1 {Ó}{{\'O}}1 {Ú}{{\'U}}1
|
|
|
{à}{{\`a}}1 {è}{{\`e}}1 {ì}{{\`i}}1 {ò}{{\`o}}1 {ù}{{\`u}}1
|
|
|
{À}{{\`A}}1 {È}{{\'E}}1 {Ì}{{\`I}}1 {Ò}{{\`O}}1 {Ù}{{\`U}}1
|
|
|
{ä}{{\"a}}1 {ë}{{\"e}}1 {ï}{{\"i}}1 {ö}{{\"o}}1 {ü}{{\"u}}1
|
|
|
{Ä}{{\"A}}1 {Ë}{{\"E}}1 {Ï}{{\"I}}1 {Ö}{{\"O}}1 {Ü}{{\"U}}1
|
|
|
{â}{{\^a}}1 {ê}{{\^e}}1 {î}{{\^i}}1 {ô}{{\^o}}1 {û}{{\^u}}1
|
|
|
{Â}{{\^A}}1 {Ê}{{\^E}}1 {Î}{{\^I}}1 {Ô}{{\^O}}1 {Û}{{\^U}}1
|
|
|
{œ}{{\oe}}1 {Œ}{{\OE}}1 {æ}{{\ae}}1 {Æ}{{\AE}}1 {ß}{{\ss}}1
|
|
|
{ç}{{\c c}}1 {Ç}{{\c C}}1 {ø}{{\o}}1 {å}{{\r a}}1 {Å}{{\r A}}1
|
|
|
{€}{{\EUR}}1 {£}{{\pounds}}1
|
|
|
%
|
|
|
{^}{{{\color{ipython_purple}\^{}}}}1
|
|
|
{=}{{{\color{ipython_purple}=}}}1
|
|
|
%
|
|
|
{+}{{{\color{ipython_purple}+}}}1
|
|
|
{*}{{{\color{ipython_purple}$^\ast$}}}1
|
|
|
{/}{{{\color{ipython_purple}/}}}1
|
|
|
%
|
|
|
{+=}{{{+=}}}1
|
|
|
{-=}{{{-=}}}1
|
|
|
{*=}{{{$^\ast$=}}}1
|
|
|
{/=}{{{/=}}}1,
|
|
|
literate=
|
|
|
*{-}{{{\color{ipython_purple}-}}}1
|
|
|
{?}{{{\color{ipython_purple}?}}}1,
|
|
|
%
|
|
|
identifierstyle=\color{black}\ttfamily,
|
|
|
commentstyle=\color{ipython_red}\ttfamily,
|
|
|
stringstyle=\color{ipython_red}\ttfamily,
|
|
|
keepspaces=true,
|
|
|
showspaces=false,
|
|
|
showstringspaces=false,
|
|
|
%
|
|
|
rulecolor=\color{ipython_frame},
|
|
|
frame=single,
|
|
|
frameround={t}{t}{t}{t},
|
|
|
framexleftmargin=6mm,
|
|
|
numbers=left,
|
|
|
numberstyle=\tiny\color{halfgray},
|
|
|
%
|
|
|
%
|
|
|
backgroundcolor=\color{ipython_bg},
|
|
|
% extendedchars=true,
|
|
|
basicstyle=\scriptsize,
|
|
|
keywordstyle=\color{ipython_green}\ttfamily,
|
|
|
morekeywords = [3]{Int, Double},
|
|
|
morekeywords = [2]{foldRight, case},
|
|
|
keywordstyle = [3]{\color{ipython_purple}\ttfamily},
|
|
|
keywordstyle = [2]{\color{ipython_cyan}\ttfamily},
|
|
|
}
|
|
|
|
|
|
\usepackage[style=authoryear, backend=bibtex]{biblatex}
|
|
|
\urlstyle{same}
|
|
|
\bibliography{bibliograpy.bib}
|
|
|
\numberwithin{figure}{section}
|
|
|
\numberwithin{table}{section}
|
|
|
\numberwithin{equation}{section}
|
|
|
|
|
|
\sectionfont{\centering}
|
|
|
\input{insbox}
|
|
|
|
|
|
%\parindent0in
|
|
|
\pagestyle{plain}
|
|
|
\thispagestyle{plain}
|
|
|
\newtheorem{Theorem}{Theorem}[section]
|
|
|
\newtheorem{Definition}[Theorem]{Definition}
|
|
|
\newtheorem{Lemma}[Theorem]{Lemma}
|
|
|
\newtheorem{Algorithm}[Theorem]{Algorithm}
|
|
|
\newtheorem{Example}[Theorem]{Example}
|
|
|
\newtheorem{Assumption}[Theorem]{Assumption}
|
|
|
|
|
|
|
|
|
\DeclareMathOperator*{\plim}{\mathbb{P}\text{-}\lim}
|
|
|
\DeclareMathOperator{\supp}{supp}
|
|
|
\DeclareMathOperator*{\argmin}{arg\,min}
|
|
|
\DeclareMathOperator*{\po}{\mathbb{P}\text{-}\mathcal{O}}
|
|
|
\DeclareMathOperator*{\equals}{=}
|
|
|
\begin{document}
|
|
|
|
|
|
|
|
|
|
|
|
\newcommand{\plimn}[0]{\plim\limits_{n \to \infty}}
|
|
|
\newcommand{\norm}[1]{\left\lVert#1\right\rVert}
|
|
|
\newcommand*\circled[1]{\tikz[baseline=(char.base)]{
|
|
|
\node[shape=circle,draw,inner sep=2pt] (char) {#1};}}
|
|
|
|
|
|
|
|
|
\newcommand{\abs}[1]{\ensuremath{\left\vert#1\right\vert}}
|
|
|
|
|
|
\newcommand\Tstrut{\rule{0pt}{2.6ex}} % = `top' strut
|
|
|
\newcommand\Bstrut{\rule[-0.9ex]{0pt}{0pt}} % = `bottom' strut
|
|
|
|
|
|
\SetKwInput{KwInput}{Input}
|
|
|
|
|
|
%\newcommand{\myrightarrow}[1]{\xrightarrow{\makebox[2em][c]{$\scriptstyle#1$}}}
|
|
|
|
|
|
%Arndt Tobias \hfill 21.12.2017\newline
|
|
|
%\textbf{Seminar Machine--Learning: Unsupervised %Learning} \newline
|
|
|
%Institut für Mathematik der Universität %Augsburg\\
|
|
|
%Lehrstuhl für Rechnerorientierte Statistik und %Datenanalyse\\
|
|
|
|
|
|
\begin{center}
|
|
|
\huge \textbf{Master Thesis}\\
|
|
|
\vspace{1cm}
|
|
|
\Large \textbf{University Augsburg\\Department of Mathematics\\Chair of
|
|
|
Computational Statistics and Data Analysis}
|
|
|
\vspace{1cm}
|
|
|
\end{center}
|
|
|
|
|
|
\begin{figure}[h]
|
|
|
\centering
|
|
|
\includegraphics[scale=1.3]{Figures/Uni_Aug_Siegel_32Grad_schwarz.png}
|
|
|
\end{figure}
|
|
|
|
|
|
\begin{center}
|
|
|
\vspace{1cm}
|
|
|
\huge \textbf{TITLE Neural Network bla blub langer Titel}\\
|
|
|
\vspace{1cm}
|
|
|
\huge \textbf{Tim Tobias Arndt}\\
|
|
|
\vspace{1cm}
|
|
|
\Large \textbf{October 2020}
|
|
|
\end{center}
|
|
|
|
|
|
\pagenumbering{gobble}
|
|
|
\clearpage
|
|
|
%\setcounter{tocdepth}{4}
|
|
|
\tableofcontents
|
|
|
\clearpage
|
|
|
\listoffigures
|
|
|
\listoftodos
|
|
|
\newpage
|
|
|
\pagenumbering{arabic}
|
|
|
% Introduction
|
|
|
\input{introduction}
|
|
|
|
|
|
\newpage
|
|
|
|
|
|
% Introduction Neural Networks
|
|
|
\input{introduction_nn}
|
|
|
|
|
|
\newpage
|
|
|
|
|
|
% Theorem 3.8
|
|
|
\input{theo_3_8}
|
|
|
|
|
|
\newpage
|
|
|
|
|
|
% Kapitel 4
|
|
|
\input{further_applications_of_nn}
|
|
|
|
|
|
\newpage
|
|
|
|
|
|
\printbibliography
|
|
|
|
|
|
% Appendix A
|
|
|
\input{appendixA.tex}
|
|
|
|
|
|
\end{document}
|
|
|
|
|
|
%%% Local Variables:
|
|
|
%%% mode: latex
|
|
|
%%% TeX-master: t
|
|
|
%%% End:
|