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\documentclass[../main.tex]{subfiles}
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\begin{document}
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\begin{document}
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\section{Lecture 2 - 07-04-2020}
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\chapter{Lecture 2 - 07-04-2020}
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\subsection{Argomento}
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\section{Argomento}
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Classification tasks\\
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Classification tasks\\
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Semantic label space Y\\
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Semantic label space Y\\
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Categorization Y finite and\\ small
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Categorization Y finite and\\ small
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@ -27,8 +27,8 @@ $
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Losses for regression?\\
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Losses for regression?\\
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$y$, and $\hat{y} \in \barra{R}$, \\so they are numbers!\\
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$y$, and $\hat{y} \in \barra{R}$, \\so they are numbers!\\
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One example of loss is the absolute loss: absolute difference between numbers\\
|
One example of loss is the absolute loss: absolute difference between numbers\\
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\subsection{Loss}
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\section{Loss}
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\subsubsection{Absolute Loss}
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\subsection{Absolute Loss}
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$$\ell(y,\hat{y} = | y - \hat{y} | \Rightarrow absolute \quad loss\\ $$
|
$$\ell(y,\hat{y} = | y - \hat{y} | \Rightarrow absolute \quad loss\\ $$
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--- DISEGNO ---\\\\
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--- DISEGNO ---\\\\
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Some inconvenient properties:
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Some inconvenient properties:
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\item Derivative only two values (not much informations)
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\item Derivative only two values (not much informations)
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\end{itemize}
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\end{itemize}
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\subsubsection{Square Loss}
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\subsection{Square Loss}
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$$ \ell(y,\hat{y} = ( y - \hat{y} )^2 \Rightarrow \textit{square loss}\\$$
|
$$ \ell(y,\hat{y} = ( y - \hat{y} )^2 \Rightarrow \textit{square loss}\\$$
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-- DISEGNO ---\\
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-- DISEGNO ---\\
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Derivative :
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@ -50,7 +50,7 @@ Real numbers as label $\rightarrow$ regression.\\
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Whenever taking difference between two prediction make sense (value are numbers) then we are talking about regression problem.\\
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Whenever taking difference between two prediction make sense (value are numbers) then we are talking about regression problem.\\
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Classification as categorization when we have small finite set.\\\\
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Classification as categorization when we have small finite set.\\\\
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\subsection{Example of information of square loss}
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\\
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The algorithm will be punish high more the prediction is not real. Algorithm will not get 0 and 1 because for example is impossible to get a perfect prediction.\\
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The algorithm will be punish high more the prediction is not real. Algorithm will not get 0 and 1 because for example is impossible to get a perfect prediction.\\
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This loss is useful to give this information to the algorithm.\\\\
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This loss is useful to give this information to the algorithm.\\\\
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Now we talk about labels and losses\\
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Now we talk about labels and losses\\
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\subsubsection{labels and losses}
|
\subsection{labels and losses}
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Data points: they have some semantic labels that denote some true about this data points and we want to predict this labels.\\
|
Data points: they have some semantic labels that denote some true about this data points and we want to predict this labels.\\
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We need to define what data points are: number? Strings? File? Typically they are stored in database records \\
|
We need to define what data points are: number? Strings? File? Typically they are stored in database records \\
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They can have very precise structure or more homogeneously structured \\
|
They can have very precise structure or more homogeneously structured \\
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@ -154,7 +154,7 @@ There is a way to encode a set of documents in point in a fixed dimensional
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space in such way it make sense this coordinate are comparable.\\
|
space in such way it make sense this coordinate are comparable.\\
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I can represent fields with [0,1] for Neural network for example. But they have no geometrical meaning\\
|
I can represent fields with [0,1] for Neural network for example. But they have no geometrical meaning\\
|
||||||
|
|
||||||
\subsubsection{Example TF(idf) documents encoding}
|
\subsection{Example TF(idf) documents encoding}
|
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TF encoding of docs.
|
TF encoding of docs.
|
||||||
\begin{enumerate}
|
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\item Extract where all the words from docs
|
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|
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@ -1,7 +1,7 @@
|
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\documentclass[../main.tex]{subfiles}
|
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\begin{document}
|
\begin{document}
|
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\section{Lecture 3 - 07-04-2020}
|
\chapter{Lecture 3 - 07-04-2020}
|
||||||
Data point x represented as sequences of measurement and we called this
|
Data point x represented as sequences of measurement and we called this
|
||||||
measurements features or attributes.\\
|
measurements features or attributes.\\
|
||||||
$$ x = (x_1,..., x_d) \qquad x_1 \quad \textit{feature value}
|
$$ x = (x_1,..., x_d) \qquad x_1 \quad \textit{feature value}
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@ -74,7 +74,7 @@ which we can avoid this to happen by design:
|
|||||||
We want when we run ERM choosing a good predictor with ...... PD\\\\
|
We want when we run ERM choosing a good predictor with ...... PD\\\\
|
||||||
|
|
||||||
|
|
||||||
\subsection{Overfitting}
|
\section{Overfitting}
|
||||||
We called this as overfitting: specific situation in which ‘A’ (where A is the
|
We called this as overfitting: specific situation in which ‘A’ (where A is the
|
||||||
learning algorithm) overfits if f output by A tends to have a training error much
|
learning algorithm) overfits if f output by A tends to have a training error much
|
||||||
smaller than the test error.\\
|
smaller than the test error.\\
|
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@ -84,7 +84,7 @@ Minimising training error doesn’t mean minimising test error. Overfitting is b
|
|||||||
Why this happens?\\
|
Why this happens?\\
|
||||||
This happen because we have \textbf{noise in the data}\\
|
This happen because we have \textbf{noise in the data}\\
|
||||||
|
|
||||||
\subsubsection{Noise in the data}
|
\subsection{Noise in the data}
|
||||||
|
|
||||||
Noise in the data: $y_t$ is not deterministically associated with $x_i$.\\\\
|
Noise in the data: $y_t$ is not deterministically associated with $x_i$.\\\\
|
||||||
Could be that datapoint appears more times in the same test set.
|
Could be that datapoint appears more times in the same test set.
|
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@ -160,7 +160,7 @@ define which predictor is good.\\
|
|||||||
|
|
||||||
|
|
||||||
|
|
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\subsection{Underfitting}
|
\section{Underfitting}
|
||||||
‘A’ underfits when f output by A has training error close to test error but they
|
‘A’ underfits when f output by A has training error close to test error but they
|
||||||
are both large.\\
|
are both large.\\
|
||||||
Close error test and training error is good but the are both large.
|
Close error test and training error is good but the are both large.
|
||||||
@ -183,7 +183,7 @@ $$
|
|||||||
m >> ln |F| \qquad when \quad |F| < \infty \textit{\\ where m is the size of traning set}
|
m >> ln |F| \qquad when \quad |F| < \infty \textit{\\ where m is the size of traning set}
|
||||||
$$
|
$$
|
||||||
\\
|
\\
|
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\subsection{Nearest neighbour}
|
\section{Nearest neighbour}
|
||||||
This is completely different from ERM and is one of the first learning
|
This is completely different from ERM and is one of the first learning
|
||||||
algorithm. This exploit the geometry of the data.
|
algorithm. This exploit the geometry of the data.
|
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Assume that our data space X is:
|
Assume that our data space X is:
|
||||||
|
@ -1,7 +1,7 @@
|
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|
\documentclass[../main.tex]{subfiles}
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||||||
\begin{document}
|
\begin{document}
|
||||||
\section{Lecture 4 - 07-04-2020}
|
\chapter{Lecture 4 - 07-04-2020}
|
||||||
|
|
||||||
We spoke about Knn classifier with voronoi diagram
|
We spoke about Knn classifier with voronoi diagram
|
||||||
|
|
||||||
@ -11,7 +11,7 @@ $$
|
|||||||
\\
|
\\
|
||||||
$\hnn$ predictor needs to store entire dataset.
|
$\hnn$ predictor needs to store entire dataset.
|
||||||
\\
|
\\
|
||||||
\subsection{Computing $\hnn$}
|
\section{Computing $\hnn$}
|
||||||
Computing $\hnn(x)$ requires computing distances between x and points in the traning set.
|
Computing $\hnn(x)$ requires computing distances between x and points in the traning set.
|
||||||
\\
|
\\
|
||||||
$$
|
$$
|
||||||
@ -69,7 +69,7 @@ There are some heuristic to run NN algorithm without value of $k$.
|
|||||||
\\
|
\\
|
||||||
\end{itemize}
|
\end{itemize}
|
||||||
|
|
||||||
\subsection{Tree Predictor}
|
\section{Tree Predictor}
|
||||||
If a give you data not welled defined in a Euclidean space.
|
If a give you data not welled defined in a Euclidean space.
|
||||||
\\
|
\\
|
||||||
$X = X_1 \cdot x \cdot ... \cdot X_d \cdot x$ \qquad Medical Record
|
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\documentclass[a4paper,12pt]{ElegantNote}
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%Options: Sonny, Lenny, Glenn, Conny, Rejne, Bjarne, Bjornstrup
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%\usepackage[Glenn]{fncychap}
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\newcommand\gray[1]{\textcolor{mygray}{#1}}
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%\titleformat{\chapter}[display]
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% {\normalfont\bfseries}{}{0pt}{\Large}
|
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\titleformat{\chapter}[display]
|
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|
{\normalfont\bfseries}{}{0pt}{\Huge\color{Blue}}
|
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|
\titlespacing*{\chapter}{0pt}{-80pt}{40pt}
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|
\chapterfont{\color{Blue}}
|
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\sectionfont{\color{GoodGreen}}
|
\sectionfont{\color{GoodGreen}}
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|
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|
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%\titleformat{\section}
|
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||||||
% {\normalfont\normalsize\bfseries}{\thesection.}{1em}{}
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||||||
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|
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\begin{document}
|
\begin{document}
|
||||||
|
|
||||||
\begin{titlepage}
|
\begin{titlepage}
|
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|
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|
|||||||
|
\babel@toc {english}{}
|
||||||
|
\contentsline {chapter}{\numberline {1}Lecture 1 - 09-03-2020}{2}%
|
||||||
|
\contentsline {section}{\numberline {1.1}Introduction}{2}%
|
||||||
|
\contentsline {chapter}{\numberline {2}Lecture 2 - 07-04-2020}{5}%
|
||||||
|
\contentsline {section}{\numberline {2.1}Argomento}{5}%
|
||||||
|
\contentsline {section}{\numberline {2.2}Loss}{5}%
|
||||||
|
\contentsline {subsection}{\numberline {2.2.1}Absolute Loss}{5}%
|
||||||
|
\contentsline {subsection}{\numberline {2.2.2}Square Loss}{6}%
|
||||||
|
\contentsline {subsection}{\numberline {2.2.3}Example of information of square loss}{6}%
|
||||||
|
\contentsline {subsection}{\numberline {2.2.4}labels and losses}{7}%
|
||||||
|
\contentsline {subsection}{\numberline {2.2.5}Example TF(idf) documents encoding}{9}%
|
||||||
|
\contentsline {chapter}{\numberline {3}Lecture 3 - 07-04-2020}{11}%
|
||||||
|
\contentsline {section}{\numberline {3.1}Overfitting}{13}%
|
||||||
|
\contentsline {subsection}{\numberline {3.1.1}Noise in the data}{13}%
|
||||||
|
\contentsline {section}{\numberline {3.2}Underfitting}{14}%
|
||||||
|
\contentsline {section}{\numberline {3.3}Nearest neighbour}{15}%
|
||||||
|
\contentsline {chapter}{\numberline {4}Lecture 4 - 07-04-2020}{17}%
|
||||||
|
\contentsline {section}{\numberline {4.1}Computing $h_{NN}$}{17}%
|
||||||
|
\contentsline {section}{\numberline {4.2}Tree Predictor}{18}%
|
||||||
|
\contentsline {chapter}{\numberline {5}Lecture 5 - 07-04-2020}{21}%
|
||||||
|
\contentsline {section}{\numberline {5.1}Tree Classifier}{21}%
|
||||||
|
\contentsline {section}{\numberline {5.2}Jensen’s inequality}{22}%
|
||||||
|
\contentsline {section}{\numberline {5.3}Tree Predictor}{24}%
|
||||||
|
\contentsline {section}{\numberline {5.4}Statistical model for Machine Learning}{25}%
|
||||||
|
\contentsline {chapter}{\numberline {6}Lecture 6 - 07-04-2020}{27}%
|
||||||
|
\contentsline {chapter}{\numberline {7}Lecture 7 - 07-04-2020}{28}%
|
||||||
|
\contentsline {chapter}{\numberline {8}Lecture 8 - 07-04-2020}{29}%
|
||||||
|
\contentsline {chapter}{\numberline {9}Lecture 9 - 07-04-2020}{30}%
|
||||||
|
\contentsline {chapter}{\numberline {10}Lecture 10 - 07-04-2020}{31}%
|
||||||
|
\contentsline {section}{\numberline {10.1}TO BE DEFINE}{31}%
|
Loading…
Reference in New Issue
Block a user