update ML notes

1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/NO/bibliography.bib

@@ -0,0 +1,13 @@
+@book
+{
+    AM69,
+    AUTHOR = {Atiyah, M. F. and Macdonald, I. G.},
+     TITLE = {Introduction to commutative algebra},
+ PUBLISHER = {Addison-Wesley Publishing Co., Reading, Mass.-London-Don
+              Mills, Ont.},
+      YEAR = {1969},
+     PAGES = {ix+128},
+   MRCLASS = {13.00},
+  MRNUMBER = {0242802 (39 \#4129)},
+MRREVIEWER = {J. A. Johnson},
+}

1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/NO/figures/ball.tex

@@ -0,0 +1,6 @@
+\documentclass[tikz]{standalone}
+\begin{document}
+    \begin{tikzpicture}
+          \draw[shading = ball] (0, 0) circle (2);
+    \end{tikzpicture}
+\end{document}

1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/NO/figures/balls.tex

@@ -0,0 +1,7 @@
+\documentclass[tikz]{standalone}
+\begin{document}
+    \begin{tikzpicture}
+          \draw[shading = ball] (0, 0) circle (2);
+          \draw[shading = ball] (5, 0) circle (2);
+    \end{tikzpicture}
+\end{document}

1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/NO/main.tex

@@ -0,0 +1,60 @@
+\documentclass[a4paper, british]{memoir}
+
+\usepackage{style}       % Custom style
+\usepackage{mnfrontpage} % Front page
+\usepackage{kantlipsum}  % Dummy text
+
+\title{Title}
+\subtitle{Optional Subtitle}
+\author{First Author \and Second Author}
+\kind{Report \#17\hfill\the\year} % Optional
+
+\includeonly
+{
+    sections/abstract,
+    sections/acknowledgements,
+    sections/introduction,
+    sections/chapter2,
+    sections/chapter3,
+    sections/chapter4,
+    sections/appendixA,
+    sections/appendixB,
+}
+
+\begin{document}
+
+    \frontmatter        % Folios in Roman numerals, unnumbered chapters.
+
+    \mnfrontpage
+
+    \include{sections/abstract}
+    \include{sections/acknowledgements}
+
+    \cleartorecto
+    \tableofcontents    % Or \tableofcontents*
+    \cleartorecto
+    \listoffigures      % Or \listoffigures*
+    \cleartorecto
+    \listoftables       % Or \listoftables*
+
+    \mainmatter         % Folios in Arabic numerals, numbered chapters.
+
+    \include{sections/introduction}
+
+    \part{The First Part}
+
+    \include{sections/chapter2}
+    \include{sections/chapter3}
+    \include{sections/chapter4}
+
+    \appendix           % "Chapter" is renamed "Appendix"
+    \appendixpage       % Similar to \part*{Appendices}, but appears in TOC.
+
+    \include{sections/appendixA}
+    \include{sections/appendixB}
+
+    \backmatter         % Folios in Arabic numerals, unnumbered chapters.
+
+    \printbibliography
+
+\end{document}

1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/NO/mnfrontpage.sty

@@ -0,0 +1,387 @@
+% Package for creating front pages
+% Implemented by Martin Helsø (martibhe@math.uio.no).
+% Version 2015-12-21.
+
+%% Identification part:
+
+\NeedsTeXFormat{LaTeX2e}[1994/12/01]
+
+\ProvidesClass{mnfrontpage}
+
+%% Standard headers:
+
+\DeclareOption{american} { \def \MNFP@lang {eng} }
+\DeclareOption{english}  { \def \MNFP@lang {eng} }
+\DeclareOption{UKenglish}{ \def \MNFP@lang {eng} }
+\DeclareOption{USenglish}{ \def \MNFP@lang {eng} }
+\DeclareOption{norsk}    { \def \MNFP@lang {bm}  }
+\DeclareOption{nynorsk}  { \def \MNFP@lang {nn}  }
+
+%% Department:
+
+\DeclareOption{MatNat}
+{ 
+    \def \MNFP@Dept {mn}  
+    \def \MNFP@nr   {1}    
+}
+\DeclareOption{FRM}
+{ 
+    \def \MNFP@Dept {frm}  
+    \def \MNFP@nr   {2}    
+}
+\DeclareOption{FYS}
+{ 
+    \def \MNFP@Dept {fys}  
+    \def \MNFP@nr   {3}    
+}
+\DeclareOption{IBV}
+{ 
+    \def \MNFP@Dept {ibv}  
+    \def \MNFP@nr   {4}    
+}
+\DeclareOption{GEO}
+{ 
+    \def \MNFP@Dept {geo}  
+    \def \MNFP@nr   {5}    
+}
+\DeclareOption{IFI}
+{ 
+    \def \MNFP@Dept {ifi}  
+    \def \MNFP@nr   {6}    
+}
+\DeclareOption{AST}
+{ 
+    \def \MNFP@Dept {ast}  
+    \def \MNFP@nr   {7}    
+}
+\DeclareOption{KJM}
+{ 
+    \def \MNFP@Dept {kjm}  
+    \def \MNFP@nr   {8}    
+}
+\DeclareOption{MAT}
+{ 
+    \def \MNFP@Dept {mat}  
+    \def \MNFP@nr   {9}    
+}
+
+%% Background: 
+
+\DeclareOption{1} { \def \MNFP@nr  {1} }
+\DeclareOption{2} { \def \MNFP@nr  {2} } 
+\DeclareOption{3} { \def \MNFP@nr  {3} } 
+\DeclareOption{4} { \def \MNFP@nr  {4} }
+\DeclareOption{5} { \def \MNFP@nr  {5} } 
+\DeclareOption{6} { \def \MNFP@nr  {6} } 
+\DeclareOption{7} { \def \MNFP@nr  {7} }
+\DeclareOption{8} { \def \MNFP@nr  {8} } 
+\DeclareOption{9} { \def \MNFP@nr  {9} } 
+\DeclareOption{10}{ \def \MNFP@nr {10} }
+
+%% Purpose of document:
+
+\DeclareOption{web}  
+{ 
+    \def \MNFP@indent { 0 mm}
+    \def \MNFP@type     {web}
+}
+\DeclareOption{print}
+{
+    \def \MNFP@indent { 0 mm}
+    \def \MNFP@type   {print}
+}
+\DeclareOption{bound}
+{ 
+    \def \MNFP@indent {11 mm}
+    \def \MNFP@type   {print}
+}
+
+
+%% Length of titles:
+
+\DeclareOption{OrdinaryTitle}
+{ 
+    \def \MNFP@title {Ordinary}
+    \def \MNFP@titlesize {\fontsize{32}{35pt}} 
+}
+\DeclareOption{LongTitle}
+{ 
+    \def \MNFP@title {Long}
+    \def \MNFP@titlesize {\fontsize{24}{27pt}}
+}
+\DeclareOption{ExtraLongTitle}
+{
+    \def \MNFP@title {ExtraLong} 
+    \def \MNFP@titlesize {\fontsize{17}{20pt}}
+}
+
+\DeclareOption{BlankPage}    { \def \MNFP@secondpage {blank}    }
+\DeclareOption{OnlyFrontpage}{ \def \MNFP@secondpage {}         }
+
+%% Masther's thesis
+
+\DeclareOption{compendium}{ \def \MNFP@thesis {} }
+\DeclareOption{master}    { \def \MNFP@thesis {thesis} }
+
+%% Standard options:
+
+\ExecuteOptions{english}
+\ExecuteOptions{MatNat}
+\ExecuteOptions{web}
+\ExecuteOptions{OrdinaryTitle}
+\ExecuteOptions{BlankPage}
+\ExecuteOptions{compendium}
+\ProcessOptions\relax
+
+%% Initial code:
+
+\RequirePackage[T1]{fontenc}
+\RequirePackage{calc}
+\RequirePackage{eso-pic}
+\RequirePackage{picture}
+\RequirePackage{xifthen}
+\RequirePackage{tikz}
+\RequirePackage{fix-cm}
+    
+\definecolor{bannergrey}{cmyk}{0, 0, 0, 0.3}
+
+%% The main command:
+
+\@ifclassloaded{memoir}
+{
+    \newcommand{\mnfrontpage}
+    {
+        \def \and {\leavevmode\unskip, }
+        \begin{titlingpage}
+            \AddToShipoutPictureBG*{\MNFP@print@background}
+            \AddToShipoutPictureFG*{\MNFP@print@title}
+            \null
+        \end{titlingpage}
+    }    
+}
+{
+    \newcommand{\mnfrontpage}
+    {
+        \def \and {\leavevmode\unskip, }
+        \begin{titlepage}
+            \AddToShipoutPictureBG*{\MNFP@print@background}
+            \AddToShipoutPictureFG*{\MNFP@print@title}
+            \null
+        \end{titlepage}
+        \ifthenelse{ \equal{\MNFP@secondpage}{blank} }
+        {
+            \MNFP@blankpage
+        }
+        {}
+    }
+}
+
+%% Additional commands:
+
+\newcommand{\subtitle}[1]{ \def \MNFP@subtitle{#1} }
+\subtitle{}
+
+\newcommand{\kind}[1]{ \def \MNFP@kind{#1} }
+\ifthenelse{ \equal{\MNFP@thesis}{thesis} }
+{
+    %% Define a suitable document kind, like "Master's Thesis, Spring 2016":
+    \kind
+    {
+        \csname MNFP@thesisname@\MNFP@lang\endcsname,~\MNFP@term~\MNFP@year
+    }
+}
+{
+    \kind{}
+}
+
+%% Include the title page background:
+
+\newcommand{\MNFP@print@background}
+{
+    \put(-3 bp, 0 bp)
+    {
+        \includegraphics
+            {mnfrontpage-images/mnfrontpage-bg-\MNFP@type-\MNFP@nr}
+    }
+    
+    \put(-3 mm, 142 mm)
+    {
+        \begin{tikzpicture}[scale = 1mm]
+            \filldraw[white, opacity = 0.8] 
+                (0, 2.5) rectangle (\paperwidth, 3.73);
+            \filldraw[white, opacity = 0.6] 
+                (0, 0) rectangle (\paperwidth, 2.5);
+            \filldraw[bannergrey, opacity = 0.7] 
+                (0, 0) rectangle (\paperwidth, 2.5);
+        \end{tikzpicture}
+    }
+    
+    \put(25 mm + \MNFP@indent, 25 mm)
+    {
+        \includegraphics[width = 27mm]
+            {mnfrontpage-images/mnfrontpage-apollon}
+    }
+    
+    \ifthenelse{ \equal{\MNFP@Dept}{mn} }
+    {
+        \put(22 mm + \MNFP@indent, 220 mm)
+        {
+            \includegraphics[scale = 0.5]
+                {mnfrontpage-images/mnfrontpage-logo-\MNFP@Dept-\MNFP@lang}
+        }
+    }
+    {
+        \put(19 mm + \MNFP@indent, 222 mm)
+        {
+            \includegraphics[scale = 0.6]
+                {mnfrontpage-images/mnfrontpage-logo-\MNFP@Dept-\MNFP@lang}
+        }
+    }
+}
+    
+%% Include the title, subtitle, author and date:
+
+\newcommand{\MNFP@print@title}
+{
+    {
+        \newlength{\MNFPtitlelength}
+        
+        \ifthenelse{ \equal{\MNFP@Dept}{mn} }
+        {
+            \def \MNFP@titlepos {41.5 mm}
+            \setlength{\MNFPtitlelength}
+                {\paperwidth - 22 mm - \MNFP@titlepos - \MNFP@indent} 
+        }
+        {
+            \def \MNFP@titlepos {42.4 mm}
+            \setlength{\MNFPtitlelength}
+                {\paperwidth - 19 mm - \MNFP@titlepos - \MNFP@indent} 
+        }
+        
+        \put(\MNFP@titlepos + \MNFP@indent, 141.5 mm)
+        {
+            \vbox to 7.15cm 
+            {
+                \hsize = \MNFPtitlelength
+                \raggedright
+                
+                % Redefinition of standard \LaTeX command because
+                % the font package 'bera' mangles it!
+                \ifthenelse{ \isundefined{\fveLaTeX} }{}
+                {
+                    \DeclareRobustCommand{\mn@LaTeX}
+                    {
+                        L\kern-.36em
+                        {
+                            \sbox\z@ T
+                            \vbox to\ht\z@
+                            {
+                                \hbox
+                                {
+                                    \check@mathfonts
+                                    \fontsize\sf@size\z@
+                                    \math@fontsfalse\selectfont
+                                    A
+                                }
+                                \vss
+                            }
+                        }
+                        \kern-.15em
+                        \TeX
+                    }
+                    \let \LaTeX = \mn@LaTeX
+                }
+                
+                \vfill                       
+                
+                \fontfamily{\MNFP@font}
+                \MNFP@titlesize
+                \selectfont 
+                \bfseries 
+                \@title
+                
+                \newlength{\MNFP@titlelength}
+                \settowidth{\MNFP@titlelength}{\@title}
+                
+                \ifthenelse
+                { 
+                    \equal{\MNFP@title}{Ordinary} 
+                    \AND 
+                    \lengthtest{\MNFP@titlelength < \hsize}
+                }
+                {
+                    \def \MNFP@skip{2.5 em}				
+                }
+                {
+                    \def \MNFP@skip{1.5 em}
+                }
+                
+                \vskip 0.5ex
+                
+                \normalfont
+                \fontfamily{\MNFP@font}
+                \fontsize{17}{20pt}
+                \selectfont
+                \MNFP@subtitle
+                
+                \vskip \MNFP@skip
+                
+                {
+                    \bfseries
+                    \ifdefined\authors
+                        \authors
+                    \else
+                        \@author
+                    \fi
+                }
+                \\[0.1ex] 
+                \MNFP@kind
+                
+                \vfill
+            }
+        }
+    }
+}
+
+
+%% Find the best font:
+
+\newcommand{\MNFP@font}{phv}         % Helvetica is always available, but use
+\IfFileExists{t1ua1.fd}{\renewcommand{\MNFP@font}{ua1}}{} % Arial if possible.
+
+%% Determine the term (as in "Spring 2016"):
+
+\newcounter{MNFP@cur@year}   
+\newcounter{MNFP@cur@month}
+\setcounter{MNFP@cur@year} { \the\year  }
+\setcounter{MNFP@cur@month}{ \the\month }
+
+\ifthenelse{ \theMNFP@cur@month < 7 }
+{
+    \newcommand{\MNFP@term@eng}{Spring}
+    \newcommand{\MNFP@term@bm} {v\aa ren}
+    \newcommand{\MNFP@term@nn} {v\aa ren}
+}
+{
+    \newcommand{\MNFP@term@eng}{Autumn}
+    \newcommand{\MNFP@term@bm} {h\o sten}
+    \newcommand{\MNFP@term@nn} {hausten}
+}
+    
+\newcommand{\MNFP@term}{ \csname MNFP@term@\MNFP@lang\endcsname }
+\newcommand{\MNFP@year}{ \arabic{MNFP@cur@year}               }
+
+%% Specify "Master's Thesis" in the correct language:
+
+\newcommand{\MNFP@thesisname@eng}{Master's Thesis}
+\newcommand{\MNFP@thesisname@bm} {Masteroppgave}
+\newcommand{\MNFP@thesisname@nn} {Masteroppg\aa ve}
+
+\newcommand{\MNFP@blankpage}
+{
+    \thispagestyle{empty}
+    \null
+    \newpage
+}
+
+\endinput

1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/NO/sections/abstract.tex

@@ -0,0 +1,3 @@
+\chapter{Abstract}
+\kant[1] % Dummy text
+\todo[inline]{Add new section about results in \cref{sec:fourth}.}

1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/NO/sections/acknowledgements.tex

@@ -0,0 +1,5 @@
+\chapter{Acknowledgements}
+
+\kant[2] % Dummy text
+\todo[noline]{Rewrite this.}
+\kant[3] % Dummy text

1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/NO/sections/appendixA.tex

@@ -0,0 +1,7 @@
+\chapter{The First Appendix}
+\label{sec:first-app}
+\kant[20-21] % Dummy text
+\section{First Section}
+\kant[22]    % Dummy text
+\section{Second Section}
+\kant[23-24] % Dummy text

1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/NO/sections/appendixB.tex

@@ -0,0 +1,3 @@
+\chapter{The Second Appendix}
+\label{sec:second-app}
+\kant[25-29] % Dummy text

1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/NO/sections/chapter2.tex

@@ -0,0 +1,14 @@
+\chapter{The Second Chapter}
+\label{sec:second}
+
+\kant[7-11] % Dummy text
+
+\begin{theorem}[{\cite[95]{AM69}}]
+    \label{thm:dedekind}
+    Let \( A \) be a Noetherian domain of dimension one. Then the following are equivalent:
+    \begin{enumerate}
+        \item \( A \) is integrally closed;
+        \item Every primary ideal in \( A \) is a prime power;
+        \item Every local ring \( A_\mathfrak{p} \) \( (\mathfrak{p} \neq 0) \) is a discrete valuation ring.
+    \end{enumerate}
+\end{theorem}

1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/NO/sections/chapter3.tex

@@ -0,0 +1,7 @@
+\chapter{The Third Chapter}
+\label{sec:third}
+\kant[12-13] % Dummy text
+\section{First Section}
+\kant[14]    % Dummy text
+\section{Second Section}
+\kant[15]    % Dummy text

1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/NO/sections/chapter4.tex

@@ -0,0 +1,3 @@
+\chapter{The Fourth Chapter}
+\label{sec:fourth}
+\kant[15-19] % Dummy text

1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/NO/sections/introduction.tex

@@ -0,0 +1,141 @@
+\chapter{Introduction}
+\label{sec:intro}
+
+\kant[4] % Dummy text
+
+\begin{equation}
+    \iint_D \diff x \diff y
+    =
+    \int_0^{2\pi} \int_0^t \rho \diff \rho \diff t
+    =
+    \frac{4}{3} \pi^3.
+\end{equation}
+
+\section{Figures and Tables}
+
+% Standalone with \input:
+\begin{figure}[htbp]
+    \centering
+    \input{figures/ball}
+    \caption[One ball]{One ball.}
+\end{figure}
+
+% Standalone with \includegraphics:
+\begin{figure}[thbp]
+    \centering
+    \includegraphics{balls}
+    \caption[Two balls]{Two balls.}
+\end{figure}
+
+% Todonotes:
+\begin{figure}[hbp]
+    \centering
+    \missingfigure{Three balls.}
+    \caption[Three balls]{Three balls.}
+\end{figure}
+
+\kant[5-6] % Dummy text
+
+% Booktabs:
+\begin{table}[htbp]
+    \centering
+    \begin{tabular}{@{}ll@{}}
+        \toprule
+        \textbf{Correct}               & \textbf{Incorrect}      \\
+        \midrule
+        \( \varphi \colon X \to Y \)   & \( \varphi : X \to Y \) \\[0.5ex]
+        \( \varphi(x) \coloneqq x^2 \) & \( \varphi(x) := x^2 \) \\
+        \bottomrule
+    \end{tabular}
+    \caption[Colons]{Proper colon usage.}
+\end{table}
+
+\begin{table}[htbp]
+    \centering
+    \begin{tabular}{@{}ll@{}}
+        \toprule
+        \textbf{Correct}     & \textbf{Incorrect}         \\
+        \midrule
+        \( A \implies B \)   & \( A \Rightarrow B \)      \\
+        \( A \impliedby B \) & \( A \Leftarrow B \)       \\
+        \( A \iff B \)       & \( A \Leftrightarrow B \)  \\
+        \bottomrule
+    \end{tabular}
+    \caption[Arrows]{Proper arrow usage.}
+\end{table}
+
+% Tablefootnote and multirow:
+\begin{table}[htbp]
+    \centering
+    \begin{tabular}{@{}ll@{}}
+        \toprule
+        \textbf{Correct}
+        & 
+        \textbf{Incorrect}
+        \\
+        \midrule
+        \( -1 \) 
+        & 
+        -1
+        \\[0.3ex]
+        1--10
+        &
+        1-10
+        \\[0.3ex]
+        Birch--Swinnerton-Dyer\tablefootnote{It is now easy to tell that Birch and Swinnerton-Dyer are two people.} conjecture
+        &
+        Birch-Swinnerton-Dyer conjecture
+        \\[0.3ex]
+        The ball \dash which is blue \dash is round.
+        &
+        \multirow{ 2}{*}{The ball - which is blue - is round.}
+        \\[0.3ex]
+        The ball---which is blue---is round. 
+        &
+        \\
+        \bottomrule
+    \end{tabular}
+    \caption[Dashes]{Proper dash usage.}
+\end{table}
+
+\begin{table}[hbtp]
+    \centering
+    \begin{tabular}{@{}*{2}{p{0.5\textwidth}}@{}}
+        \toprule
+        \textbf{Correct} &  \textbf{Incorrect}
+        \\
+        \midrule
+        \enquote{This is an \enquote{inner quote} inside an outer quote}
+        &
+        'This is an "inner quote" inside an outer quote'
+        \\
+        \bottomrule
+    \end{tabular}
+    \caption[Quotation marks]
+    {Proper quotation mark usage.
+    The \texttt{\textbackslash enquote} command chooses the correct
+    quotation marks for the specified language.}
+\end{table}
+
+\section{Outline}
+
+The rest of the text is organised as follows:
+\begin{description}
+    \item[\cref{sec:second}]
+    is second to none, with the notable exception of \cref{sec:intro}.
+    The main tool introduced here is the employment of unintelligible sentences.
+
+    \item[\cref{sec:third}]
+    asserts the basic properties of being the third chapter of a text.
+    This section reveals the shocking truth of filler content.
+
+    \item[\cref{sec:fourth}]
+    demonstrates how easily one can get to four chapters by simply using the \texttt{kantlipsum} package to generate dummy words.
+
+    \item[\cref{sec:first-app}]
+    features additional material for the specially interested.
+
+    \item[\cref{sec:second-app}]
+    consists of results best relegated to the back of the document,
+    ensuring that nobody will ever read it.
+\end{description}

1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/NO/style.sty

@@ -0,0 +1,320 @@
+\NeedsTeXFormat{LaTeX2e}
+
+
+\ProvidesPackage{style}[2019/06/27 Custom LaTeX style]
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% PACKAGES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%% Silence warning about obsolete package
+\RequirePackage{silence}
+\WarningFilter{remreset}{The remreset package}
+
+
+%% Standalone
+\RequirePackage{standalone}
+
+
+%% Encoding
+\RequirePackage[utf8]{inputenx}
+\RequirePackage[T1]{fontenc}
+
+
+%% Fonts and typography
+\RequirePackage{lmodern}           % Latin Modern
+\renewcommand{\sfdefault}{phv}     % Helvetica
+\RequirePackage[scaled]{beramono}  % Bera Mono (Bitstream Vera Sans Mono)
+\RequirePackage[final]{microtype}  % Improved typography
+\pretolerance = 1000               % Relaxes parameters for line breaks
+\tolerance    = 2000               % Relaxes parameters for line breaks
+\setlength{\emergencystretch}{1em} % Relaxes parameters for line breaks
+\RequirePackage{siunitx}           % Typesetting units
+\RequirePackage{listings}          % Typesetting code
+\lstset
+{
+    basicstyle       = \ttfamily\footnotesize,
+    commentstyle     = \color{gray},
+    stringstyle      = \itshape,
+    showstringspaces = false,
+    frame            = tb
+}
+\RequirePackage[obeyspaces,
+                spaces,
+                hyphens]{url}      % Typesetting URLs
+\urlstyle{sf}
+
+
+%% Mathematics
+\RequirePackage{amssymb}    % Extra symbols
+\RequirePackage{amsthm}     % Theorem-like environments
+\RequirePackage{thmtools}   % Theorem-like environments, extends amsthm
+\RequirePackage{mathtools}  % Fonts and environments for mathematical formulae
+\RequirePackage{mathrsfs}   % Script font with \mathscr{}
+\RequirePackage{dsfont}     % Double stroke font with \mathds{}
+\RequirePackage{cancel}     % Cancel terms with \cancel, \bcancel or \xcancel
+\RequirePackage{stmaryrd}   % Brackets
+\everymath
+{
+    \ifodd\value{page}          % Allow multiline equations
+        \allowdisplaybreaks[1]  % to break across two pages:
+        \else                   % - Breaks from odd to even pages are allowed,
+        \allowdisplaybreaks[4]  %   but discouraged.
+    \fi                         % - Breaks from even to odd pages are allowed.
+}
+
+
+%% Language
+\RequirePackage{babel}
+\RequirePackage{csquotes}
+
+
+%% Graphics
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+                svgnames,
+                cmyk]{xcolor}     % Pre-defined colors
+\RequirePackage{graphicx}         % Tool for importing images
+\graphicspath{{figures/}}
+\RequirePackage{tikz}             % Drawing tool
+\usetikzlibrary{calc}
+\usetikzlibrary{intersections}
+\usetikzlibrary{decorations.markings}
+
+
+%% Organising tools
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+\RequirePackage{pgffor}                                  % For-loops
+\RequirePackage{comment}                                 % Multiline comments
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+    }
+}
+
+
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+\RequirePackage{textcomp}       % Extra symbols
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+\Crefname{conjecture}{Conjecture}{Conjectures}
+\crefname{notation}{Notation}{Notations}
+\Crefname{notation}{Notation}{Notations}
+
+
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+\DeclareMathOperator{\im}{im}
+\DeclareMathOperator{\rank}{rank}
+
+
+%% Delimiters
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1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/bibliography.bib

@@ -0,0 +1,7 @@
+@Booklet{Gil:02,
+  author       = {Joseph (Yossi) Gil},
+  TITLE        = {{\LaTeXe} for Graduate Students},
+  year         = {2002},
+  howpublished = {manuscript},
+  address      = {Haifa, Israel},
+}

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1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/main.tex

@@ -0,0 +1,273 @@
+\title{Statistical Methods for Machine Learning}
+\author{
+        Andrea Ierardi \\
+                Data Science and Economcis\\
+        Università degli Studi di Milano\\
+        
+}
+\date{\today}
+
+\documentclass[12pt]{article}
+\usepackage{amsmath}
+\usepackage{systeme}
+\usepackage{amssymb}
+\newcommand\barra[1]{\mathbb{#1}}
+
+\begin{document}
+\maketitle
+
+
+\begin{abstract}
+This is the paper's abstract \ldots
+\end{abstract}
+
+\section{Lecture 1 - 09-03-2020}
+
+\subsection{Introduction}
+This is time for all good men to come to the aid of their party!
+
+MACHINE LEARNING
+In this course we look at the principle behind design of Machine learning.
+Not just coding but have an idea of algorithm that can work with the data.
+We have to fix a mathematical framework: some statistic and mathematics.
+Work on ML on a higher level
+ML is data inference: make prediction about the future using data about the
+past
+Clustering —> grouping according to similarity
+Planning —> (robot to learn to interact in a certain environment)
+Classification —> (assign meaning to data) example: Spam filtering
+I want to predict the outcome of this individual or i want to predict whether a
+person click or not in a certain advertisement.
+Examples
+Classify data into categories:
+Medical diagnosis: data are medical records and • categories are diseases
+• Document analysis: data are texts and categories are topics
+• Image analysts: data are digital images and for categories name of objects
+in the image (but could be different).
+• Spam filtering: data are emails, categories are spam vs non spam.
+• Advertising prediction: data are features of web site visitors and categories
+could be click/non click on banners.
+Classification : Different from clustering since we do not have semantically
+classification (spam or not spam) —> like meaning of the image.
+I have a semantic label.
+Clustering: i want to group data with similarity function.
+Planning: Learning what to do next
+Clustering: Learn similarity function
+Classification: Learn semantic labels meaning of data
+Planning: Learn actions given state
+In classification is an easier than planning task since I’m able to make
+prediction telling what is the semantic label that goes with data points.
+If i can do classification i can clustering.
+If you do planning you probably classify (since you understanding meaning in
+your position) and then you can also do clustering probably.
+We will focus on classification because many tasks are about classification.
+Classify data in categories we can image a set of categories.
+For instance the tasks:
+‘predict income of a person’
+‘Predict tomorrow price for a stock’
+The label is a number and not an abstract thing.
+We can distinguish two cases:
+The label set —> set of possible categories for each data • point. For each of
+this could be finite set of abstract symbols (case of document classification,
+medical diagnosis). So the task is classification.
+• Real number (no bound on how many of them). My prediction will be a real
+number and is not a category. In this case we talk about a task of
+regression.
+Classification: task we want to give a label predefined point in abstract
+categories (like YES or NO)
+Regression: task we want to give label to data points but this label are
+numbers.
+When we say prediction task: used both for classification and regression
+tasks.
+Supervised learning: Label attached to data (classification, regression)
+Unsupervised learning: No labels attached to data (clustering)
+In unsupervised the mathematical modelling and way algorithm are score and
+can learn from mistakes is a little bit harder. Problem of clustering is harder to
+model mathematically.
+You can cast planning as supervised learning: i can show the robot which is
+the right action to do in that state. But that depends on planning task is
+formalised.
+Planning is higher level of learning since include task of supervised and
+unsupervised learning.
+Why is this important ?
+Algorithm has to know how to given the label.
+In ML we want to teach the algorithm to perform prediction correctly. Initially
+algorithm will make mistakes in classifying data. We want to tell algorithm that
+classification was wrong and just want to perform a score. Like giving a grade
+to the algorithm to understand if it did bad or really bad.
+So we have mistakes!
+Algorithm predicts and something makes a mistake —> we can correct it.
+Then algorithm can be more precisely.
+We have to define this mistake.
+Mistakes in case of classification:
+If category is the wrong one (in the simple case). We • have a binary signal
+where we know that category is wrong.
+How to communicate it?
+We can use the loss function: we can tell the algorithm whether is wrong or
+not.
+Loss function: measure discrepancy between ‘true’ label and predicted
+label.
+So we may assume that every datapoint has a true label.
+If we have a set of topic this is the true topic that document is talking about.
+It is typical in supervised learning.
+\\\\
+How good the algorithm did?
+\\
+
+\[l(y,\hat{y})\leq0 \]
+
+were $y $ is true label and $\hat{y}$ is predicted label
+\\\\
+We want to build a spam filter were $0$ is not spam and $1$ is spam and that 
+Classification task: 
+\\\\
+$f(n) = \begin{cases} 0, & \mbox{if } \hat{y} = y 
+\\ 1, & 
+\mbox{if }\hat{y} \neq y
+\end{cases}
+$
+\\\\
+The loss function is the “interface” between algorithm and data.
+So algorithm know about the data through the loss function.
+If we give a useless loss function the algorithm will not perform good: is
+important to have a good loss function.
+Spam filtering
+We have two main mistakes:
+It is the same mistake? No if i have important email and you classify as spam
+that’s bad and if you show me a spam than it’s ok.
+So we have to assign a different weight.
+Even in binary classification, mistakes are not equal.
+e Iotf.TFprIuos.uos
+True came
+razee
+Cussler aircN TASK spam ACG FIRM
+ftp.y GO
+IF F Y n is soon
+IF FEY 0 Nor spam
+ZERO CNE Cass
+n n
+Span No Seamy Binary Classification
+I 2
+FALSE PEENE Mistake Y NON SPAM J Spam
+FN Mistake i f SPAM y NO spam
+2 IF Fp Meter Airenita
+f Y F on positive
+y ye en MISTAKE
+0 otherwise
+
+
+\paragraph{Outline}
+The remainder of this article is organized as follows.
+Section~\ref{previous work} gives account of previous work.
+Our new and exciting results are described in Section~\ref{results}.
+Finally, Section~\ref{conclusions} gives the conclusions.
+
+
+\section{Lecture 10 - 07-04-2020}
+
+\subsection{TO BE DEFINE}
+
+$|E[z] = |E[|E[z|x]]$
+\\\\
+$|E[X] = \sum_{t = 1}^{m} |E[x \Pi(A\begin{small}
+t \end{small} ) ]$
+\\\\
+$x \in \mathbb{R}^d
+$
+\\
+$\mathbb{P}(Y_{\Pi(s,x)} = 1) = \\\\ \mathbb{E}[\Pi { Y_{\Pi(s,x)} = 1 } ] = \\\\
+= \sum_{t = 1}^{m} \mathbb{E}[\Pi\{Y_t = 1\} \cdot \Pi { Pi(s,x) = t}] = \\\\
+= \sum_{t = 1}^{m} \mathbb{E}[\mathbb{E}[\Pi\{Y_t = 1\} \cdot \Pi\{\Pi(s,x) = t\} | X_t]] = \\\\
+given the fact that Y_t \sim \eta(X_t) \Rightarrow give me probability \\
+Y_t = 1 and \Pi(s,x) = t are independent given X_Y (e. g. \mathbb{E}[Zx] = \mathbb{E}[x] \ast \cdot \mathbb{E}[z]\\\\
+= \sum_{t = 1}^{m} \barra{E}[\barra{E}[\Pi\{Y_t = 1\}|X_t] \cdot \barra{E} [ \Pi(s,x) = t | Xt]] = \\\\
+= \sum_{t = 1}^{m} \barra{E}[\eta(X_t) \cdot \Pi \cdot \{\Pi (s,x) = t \}] = \\\\
+= \barra{E} [ \eta(X_{\Pi(s,x)}]
+$
+
+\[ \barra{P} (Y_{\Pi(s,x)}| X=x = \barra{E}[\eta(X_\Pi (s,x))] \]
+\\\\
+
+$
+\barra{P} (Y_{\Pi(s,x)} = 1, y = -1 ) = \\\\
+= \barra{E}[\Pi\{Y_{\Pi(s,x)  }= 1\} \dot \Pi\{Y= -1|X\} ]] =  \\\\ 
+= \barra{E}[\Pi \{ Y_{\Pi(s,x)} = 1\} \cdot \Pi \{ y = -1 \} ] = \\\\
+= \barra{E}[\barra{E}[\Pi \{ Y_{\Pi(s,x)} = 1\} \cdot \Pi \{ y = -1 | X \} ]] = \\\\
+$
+
+\[ Y_{\Pi(s,x)} = 1  \quad \quad y = -1 (1- \eta(x)) \quad when \quad X = x\]
+
+$
+\\\\ = \barra{E}[\barra{E}[\Pi \{Y_\Pi(s,x)\} = 1 | X] \cdot \barra{E}[\Pi \{y = -1\} |X ]] = \\\\
+= \barra {E}[\eta_{\Pi(s,x)} \cdot (1-\eta(x))] = \\\\
+similarly: \quad \barra{P}(Y_{\Pi(s,x)} = -1 ,  y = 1) = \\
+\barra{E} [(1- \eta_{\Pi(s,x)}) \cdot \eta(x)]
+\\\\
+\barra{E} [ \ell_D (\hat{h}_s)] = \barra{P}(Y_{\Pi(s,x)} \neq y ) = 
+\\\\
+= \barra{P}(Y_{\Pi(s,x)} = 1, y = -1) + \barra{P}(Y_{Pi(s,x)} = -1, y = 1) = 
+\\\\
+= \barra{E} [\eta_{\Pi(s,x)} \cdot (1-eta(x))] + \barra{E}[( 1- \eta_{\Pi(s,x)})\cdot \eta(x)]$
+\\\\
+Make assumptions on $D_x \quad and \quad \eta$: \\
+
+
+MANCAAAAAAA ROBAAA
+\\\\
+
+$
+\eta(x') <= \eta(x) + c || X-x'|| --> euclidean distance
+\\\\
+1-\eta(x') <= 1- \eta(x) + c||X-x'||
+\\\\
+$
+
+
+$
+X' = X_{Pi(s,x)}
+\\\\
+\eta(X) \cdot (1-\eta(x')) + (1-\eta(x))\cdot \eta(x') <=
+\\\\
+<= \eta(x) \cdot((1-\eta(x))+\eta(x)\cdot c||X-x'|| + (1-\eta(x))\cdot c||X-x'|| = 
+\\\\
+= 2 \cdot \eta(x) \cdot (1- \eta(x)) + c||X-x'|| \\\\
+\barra{E}[\ell_d \cdot (\hat{h}_s)] <= 2 \cdot \barra{E} [\eta(x) - (1-\eta(x))] + c \cdot \barra(E)[||X-x_{\Pi(s,x)}||]
+$
+\\ where $<=$ mean at most
+\\\\
+Compare risk for zero-one loss
+\\
+$
+\barra{E}[min\{\eta(x),1-\eta(x)\}] = \ell_D (f*)
+\\\\
+\eta(x) \cdot( 1- \eta(X)) <= min\{\eta(x), 1-eta(x) \} \quad \forall x
+\\\\
+\barra{E}[\eta(x)\cdot(1-\eta(x)] <= \ell_D(f*)
+\\\\
+\barra{E}[\ell_d(\hat{l}_s)] <= 2 \cdot \ell_D(f*) + c \cdot \barra{E}[||X-X_{\Pi(s,x)}||]
+\\\\
+\eta(x) \in \{0,1\}
+$
+\\\\
+Depends on dimension: curse of dimensionality
+\\\\--DISEGNO--
+\\\\
+$
+\ell_d(f*) = 0 \iff min\{ \eta(x), 1-\eta(x)\} =0 \quad$ with probability = 1
+\\
+to be true $\eta(x) \in \{0,1\}$
+
+\section{Previous work}\label{previous work}
+A much longer \LaTeXe{} example was written by Gil~\cite{Gil:02}.
+
+\section{Results}\label{results}
+In this section we describe the results.
+
+\section{Conclusions}\label{conclusions}
+We worked hard, and achieved very little.
+
+\bibliographystyle{abbrv}
+\bibliography{main}
+
+\end{document}
+This is never printed