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@ -1,8 +1,9 @@
\documentclass[../main.tex]{subfiles}
\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
grow it.
@ -64,7 +65,7 @@ How is traning error going to change?
Im hoping my algorithm is not going to overfit (if training error goes to 0 also
testing error goes to 0).\\
\subsection{Jensens inequality}
\section{Jensens inequality}
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 $\psi\:[0,1]\rightarrow \barra{R}$\\
$$
@ -174,7 +175,7 @@ All this functions has this shape (concave???)\\
\\
In practise Machine Learning algorithm use GNI or entropy to control the split
\\\\
\subsection{Tree Predictor}
\section{Tree Predictor}
\begin{itemize}
\item Multi class classification $|Y| > 2$ $\longrightarrow$ \red{take majority}
\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)\\
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...\\
Its important to understand that the only way to have a guideline in which

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@ -1,4 +1,4 @@
\documentclass[12pt]{article}
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\usepackage{amsmath}
\usepackage{systeme}
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@ -6,11 +6,17 @@
\usepackage[english]{babel}
\usepackage[dvipsnames]{xcolor}
\usepackage{graphicx}
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\usepackage{sectsty}
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\newcommand\barra[1]{\mathbb{#1}}
\newcommand\hnn{h_{NN}}
@ -20,21 +26,33 @@
\newcommand\sll{S_{\ell}}
\newcommand\red[1]{\textcolor{BrickRed}{#1}}
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% {\normalfont\normalsize\bfseries}{\thesection.}{1em}{}
\begin{document}
\begin{titlepage}
\begin{center}
\vspace*{1cm}
\vspace*{0.1cm}
\Huge
\textbf{Statistical Methods for Machine Learning}
\textbf{\col{Statistical Methods for Machine Learning}{Blue}}
\vspace{0.5cm}
\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}
\textbf{Andrea Ierardi}
@ -43,16 +61,10 @@
Lecture notes
\vspace{0.8cm}
\includegraphics[width=.7\linewidth]{frontpage2}
\Large
Università degli Studi di Milano
\\
Milan\\
12/04/2020
\vspace{1cm}
\includegraphics[width=0.9\linewidth]{front}
\end{center}
\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}Jensens 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}%