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This is time for all good men to come to the aid of their party! This is time for all good men to come to the aid of their party!
MACHINE LEARNING MACHINE LEARNING

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1year/3trimester/Machine Learning, Statistical Learning, Deep Learning and Artificial Intelligence/Machine Learning/lectures/lecture2.tex
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@ -1,9 +1,9 @@
\documentclass[../main.tex]{subfiles} \documentclass[../main.tex]{subfiles}
\begin{document} \begin{document}
\section{Lecture 2 - 07-04-2020} \chapter{Lecture 2 - 07-04-2020}
\subsection{Argomento} \section{Argomento}
Classification tasks\\ Classification tasks\\
Semantic label space Y\\ Semantic label space Y\\
Categorization Y finite and\\ small Categorization Y finite and\\ small
@ -27,8 +27,8 @@ $
Losses for regression?\\ Losses for regression?\\
$y$, and $\hat{y} \in \barra{R}$, \\so they are numbers!\\ $y$, and $\hat{y} \in \barra{R}$, \\so they are numbers!\\
One example of loss is the absolute loss: absolute difference between numbers\\ One example of loss is the absolute loss: absolute difference between numbers\\
\subsection{Loss} \section{Loss}
\subsubsection{Absolute Loss} \subsection{Absolute Loss}
$$\ell(y,\hat{y} = | y - \hat{y} | \Rightarrow absolute \quad loss\\ $$ $$\ell(y,\hat{y} = | y - \hat{y} | \Rightarrow absolute \quad loss\\ $$
--- DISEGNO ---\\\\ --- DISEGNO ---\\\\
Some inconvenient properties: Some inconvenient properties:
@ -38,7 +38,7 @@ Some inconvenient properties:
\item Derivative only two values (not much informations) \item Derivative only two values (not much informations)
\end{itemize} \end{itemize}
\subsubsection{Square Loss} \subsection{Square Loss}
$$ \ell(y,\hat{y} = ( y - \hat{y} )^2 \Rightarrow \textit{square loss}\\$$ $$ \ell(y,\hat{y} = ( y - \hat{y} )^2 \Rightarrow \textit{square loss}\\$$
-- DISEGNO ---\\ -- DISEGNO ---\\
Derivative : Derivative :
@ -50,7 +50,7 @@ Real numbers as label $\rightarrow$ regression.\\
Whenever taking difference between two prediction make sense (value are numbers) then we are talking about regression problem.\\ Whenever taking difference between two prediction make sense (value are numbers) then we are talking about regression problem.\\
Classification as categorization when we have small finite set.\\\\ Classification as categorization when we have small finite set.\\\\
\subsubsection{Example of information of square loss} \subsection{Example of information of square loss}
$\ell(y,\hat{y}) = ( y - \hat{y} )^2 = F(y) $\ell(y,\hat{y}) = ( y - \hat{y} )^2 = F(y)
\\ \\
@ -106,7 +106,7 @@ $
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.\\ 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.\\
This loss is useful to give this information to the algorithm.\\\\ This loss is useful to give this information to the algorithm.\\\\
Now we talk about labels and losses\\ Now we talk about labels and losses\\
\subsubsection{labels and losses} \subsection{labels and losses}
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.\\
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 \\
They can have very precise structure or more homogeneously structured \\ They can have very precise structure or more homogeneously structured \\
@ -154,7 +154,7 @@ There is a way to encode a set of documents in point in a fixed dimensional
space in such way it make sense this coordinate are comparable.\\ space in such way it make sense this coordinate are comparable.\\
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}
TF encoding of docs. TF encoding of docs.
\begin{enumerate} \begin{enumerate}
\item Extract where all the words from docs \item Extract where all the words from docs

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@ -1,7 +1,7 @@
\documentclass[../main.tex]{subfiles} \documentclass[../main.tex]{subfiles}
\begin{document} \begin{document}
\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}
@ -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.\\
@ -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.
@ -160,7 +160,7 @@ define which predictor is good.\\
\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 @@ $$
m >> ln |F| \qquad when \quad |F| < \infty \textit{\\ where m is the size of traning set} m >> ln |F| \qquad when \quad |F| < \infty \textit{\\ where m is the size of traning set}
$$ $$
\\ \\
\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.
Assume that our data space X is: Assume that our data space X is:

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\documentclass[../main.tex]{subfiles} \documentclass[../main.tex]{subfiles}
\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 $X = X_1 \cdot x \cdot ... \cdot X_d \cdot x$ \qquad Medical Record

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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}%