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Chapter 1.
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\documentclass[../main.tex]{subfiles} \documentclass[../main.tex]{subfiles}
\begin{document} \begin{document}
\section{Lecture 5 - 07-04-2020}
\subsection{Tree Classifier} \chapter{Lecture 5 - 07-04-2020}
\section{Tree Classifier}
Supposed we groped a tree up to this point and we are wandering how to Supposed we groped a tree up to this point and we are wandering how to
grow it. grow it.
@ -64,7 +65,7 @@ How is traning error going to change?
I’m hoping my algorithm is not going to overfit (if training error goes to 0 also I’m hoping my algorithm is not going to overfit (if training error goes to 0 also
testing error goes to 0).\\ testing error goes to 0).\\
\subsection{Jensen’s inequality} \section{Jensen’s inequality}
If $\psi$ is a concave function $\longrightarrow $ (like $log$ or $\sqrt[2]{..}$ )\\ If $\psi$ is a concave function $\longrightarrow $ (like $log$ or $\sqrt[2]{..}$ )\\
Also $\psi$ is a function that map $0$ to $1$, \quad $\longrightarrow$ \quad $\psi\:[0,1]\rightarrow \barra{R}$\\ Also $\psi$ is a function that map $0$ to $1$, \quad $\longrightarrow$ \quad $\psi\:[0,1]\rightarrow \barra{R}$\\
$$ $$
@ -174,7 +175,7 @@ All this functions has this shape (concave???)\\
\\ \\
In practise Machine Learning algorithm use GNI or entropy to control the split In practise Machine Learning algorithm use GNI or entropy to control the split
\\\\ \\\\
\subsection{Tree Predictor} \section{Tree Predictor}
\begin{itemize} \begin{itemize}
\item Multi class classification $|Y| > 2$ $\longrightarrow$ \red{take majority} \item Multi class classification $|Y| > 2$ $\longrightarrow$ \red{take majority}
\item Regression $Y = \barra{R} $ $\longrightarrow$ \red{take average of labels in $\sll$} \item Regression $Y = \barra{R} $ $\longrightarrow$ \red{take average of labels in $\sll$}
@ -210,7 +211,7 @@ classifier (second one) making test splitting data space into region that has
this sort of “blackish” shape ( like boxes: blue box, red box, yellow box)\\ this sort of “blackish” shape ( like boxes: blue box, red box, yellow box)\\
A good exercise in which I want to reconstruct the tree given this picture. A good exercise in which I want to reconstruct the tree given this picture.
\\\\ \\\\
\subsection{Statistical model for Machine Learning} \section{Statistical model for Machine Learning}
To understand Tree classifier, nearest neighbour and other algorithm...\\ To understand Tree classifier, nearest neighbour and other algorithm...\\
It’s important to understand that the only way to have a guideline in which It’s important to understand that the only way to have a guideline in which

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@ -1,4 +1,4 @@
\documentclass[12pt]{article} \documentclass[a4paper,12pt]{ElegantNote}
\usepackage{amsmath} \usepackage{amsmath}
\usepackage{systeme} \usepackage{systeme}
\usepackage{amssymb} \usepackage{amssymb}
@ -6,11 +6,17 @@
\usepackage[english]{babel} \usepackage[english]{babel}
\usepackage[dvipsnames]{xcolor} \usepackage[dvipsnames]{xcolor}
\usepackage{graphicx} \usepackage{graphicx}
\usepackage{xcolor}
\usepackage{sectsty}
\usepackage{framed}
\usepackage{titlesec}
\usepackage[T1]{fontenc}
\graphicspath{ {./img/} } \graphicspath{ {./img/} }
\definecolor{mypink}{cmyk}{0, 0.7808, 0.4429, 0.1412} \definecolor{mypink}{cmyk}{0, 0.7808, 0.4429, 0.1412}
\definecolor{mygray}{gray}{0.6} \definecolor{mygray}{gray}{0.6}
\usepackage{framed} \definecolor{DarkGreen}{RGB}{0,100,0}
\definecolor{GoodGreen}{RGB}{46,139,87}
\newcommand\barra[1]{\mathbb{#1}} \newcommand\barra[1]{\mathbb{#1}}
\newcommand\hnn{h_{NN}} \newcommand\hnn{h_{NN}}
@ -20,21 +26,33 @@
\newcommand\sll{S_{\ell}} \newcommand\sll{S_{\ell}}
\newcommand\red[1]{\textcolor{BrickRed}{#1}} \newcommand\red[1]{\textcolor{BrickRed}{#1}}
\newcommand\gray[1]{\textcolor{mygray}{#1}} \newcommand\gray[1]{\textcolor{mygray}{#1}}
\newcommand\col[2]{\textcolor{#2}{#1}}
\chapterfont{\color{Blue}}
\sectionfont{\color{GoodGreen}}
\subsectionfont{\color{GoodGreen}}
%\titleformat{\section}
% {\normalfont\normalsize\bfseries}{\thesection.}{1em}{}
\begin{document} \begin{document}
\begin{titlepage} \begin{titlepage}
\begin{center} \begin{center}
\vspace*{1cm} \vspace*{0.1cm}
\Huge \Huge
\textbf{Statistical Methods for Machine Learning} \textbf{\col{Statistical Methods for Machine Learning}{Blue}}
\vspace{0.5cm} \vspace{0.5cm}
\LARGE \LARGE
Data Science and Economics Data Science and Economics \\
Università degli Studi di Milano\\
\vspace{0.5cm}
\includegraphics[width=.5\linewidth]{unimi}
\vspace{1.5cm} \vspace{1.5cm}
\textbf{Andrea Ierardi} \textbf{Andrea Ierardi}
@ -43,16 +61,10 @@
Lecture notes Lecture notes
\vspace{0.8cm} \vspace{1cm}
\includegraphics[width=.7\linewidth]{frontpage2}
\Large
Università degli Studi di Milano
\\
Milan\\
12/04/2020
\includegraphics[width=0.9\linewidth]{front}
\end{center} \end{center}
\end{titlepage} \end{titlepage}

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\babel@toc {english}{}
\contentsline {section}{\numberline {1}Lecture 1 - 09-03-2020}{3}%
\contentsline {subsection}{\numberline {1.1}Introduction}{3}%
\contentsline {section}{\numberline {2}Lecture 2 - 07-04-2020}{6}%
\contentsline {subsection}{\numberline {2.1}Argomento}{6}%
\contentsline {subsection}{\numberline {2.2}Loss}{6}%
\contentsline {subsubsection}{\numberline {2.2.1}Absolute Loss}{6}%
\contentsline {subsubsection}{\numberline {2.2.2}Square Loss}{7}%
\contentsline {subsubsection}{\numberline {2.2.3}Example of information of square loss}{7}%
\contentsline {subsubsection}{\numberline {2.2.4}labels and losses}{9}%
\contentsline {subsubsection}{\numberline {2.2.5}Example TF(idf) documents encoding}{10}%
\contentsline {section}{\numberline {3}Lecture 3 - 07-04-2020}{12}%
\contentsline {subsection}{\numberline {3.1}Overfitting}{14}%
\contentsline {subsubsection}{\numberline {3.1.1}Noise in the data}{14}%
\contentsline {subsection}{\numberline {3.2}Underfitting}{16}%
\contentsline {subsection}{\numberline {3.3}Nearest neighbour}{16}%
\contentsline {section}{\numberline {4}Lecture 4 - 07-04-2020}{18}%
\contentsline {subsection}{\numberline {4.1}Computing $h_{NN}$}{18}%
\contentsline {subsection}{\numberline {4.2}Tree Predictor}{19}%
\contentsline {section}{\numberline {5}Lecture 5 - 07-04-2020}{22}%
\contentsline {subsection}{\numberline {5.1}Tree Classifier}{22}%
\contentsline {subsection}{\numberline {5.2}Jensen’s inequality}{23}%
\contentsline {subsection}{\numberline {5.3}Tree Predictor}{25}%
\contentsline {subsection}{\numberline {5.4}Statistical model for Machine Learning}{26}%
\contentsline {section}{\numberline {6}Lecture 6 - 07-04-2020}{28}%
\contentsline {section}{\numberline {7}Lecture 7 - 07-04-2020}{29}%
\contentsline {section}{\numberline {8}Lecture 8 - 07-04-2020}{30}%
\contentsline {section}{\numberline {9}Lecture 9 - 07-04-2020}{31}%
\contentsline {section}{\numberline {10}Lecture 10 - 07-04-2020}{32}%
\contentsline {subsection}{\numberline {10.1}TO BE DEFINE}{32}%