notes-intro-to-stat-learning/notes.tex

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\hypersetup{pdftitle={Notes for "An Introduction to Statistical Learning"},
 pdfauthor={Zelphir Kaltstahl},
 pdfsubject={statistical learning},
 pdfkeywords={statistical learning}}

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\begin{document}
\title{Notes for ``An Introduction to Statistical Learning''}

\maketitle
\tableofcontents{}\pagebreak{}

\section{macros (ignore this section in PDF)}
\begin{itemize}
\item bold math symbol: 
\global\long\def\mathbold#1{\bm{{#1}}}%
\item big parentheses wrapping an expression: 
\global\long\def\paren#1{\left(#1\right)}%
\item $\paren{\frac{\frac{1}{2}}{3}}$
\end{itemize}

\section{Definitions}
\begin{description}
\item [{Supervised\ Learning}] analyzing an input to output relationship
to make predictions or estimations about future outputs
\item [{Unsupervised\ Learning}] learn structures and relationships from
data
\item [{Regression}] prediction of continuous or quantitative values
\item [{Classification}] prediction of categorical or qualitative values
\item [{Clustering}] grouping input data points, without predicting an
output value
\item [{Principal\ component}] todo
\item [{Dimension}] todo
\item [{Observation}] (see data point)
\item [{Input\ variable}] one attribute of a data set
\item [{Data\ point}] tuple of all input variables
\end{description}

\section{Mathematical notation of the book}
\begin{itemize}
\item $n$: number of (distinct) data points
\item $p$: number of input variables
\item $x_{ij}$: row-major interpretation: select from the data set $\mathbold X$
the $i$-th data point, $j$-th variable, indexing starting at $1$
\item $x_{i}$: select from the data set $\mathbold X$ the $i$-th data
point, which will be a vector: $x_{i}=\paren{\begin{array}{c}
x_{i1}\\
x_{i2}\\
\vdots\\
x_{ip}
\end{array}}$
\item $\mathbold{x_{j}}$: (note the bold in contrast to $x_{i}$!) column
$j$ of data set $\mathbold X$
\item $x^{T}$: transpose $x$
\item $\mathbold X$: matrix of $n$ rows and $p$ columns: 
\begin{align*}
\mathbold{X=\paren{\begin{array}{cccc}
x_{11} & x_{12} & \dots & x_{1p}\\
x_{21} & x_{22} & \dots & x_{2p}\\
\vdots & \vdots & \ddots & \vdots\\
x_{n1} & x_{n2} & \dots & x_{np}
\end{array}}} & =(\mathbold{x_{1}},\mathbold{x_{2}},\dots,\mathbold{x_{p}})=\begin{pmatrix}x_{1}^{T}\\
x_{2}^{T}\\
\vdots\\
x_{n}^{T}
\end{pmatrix}
\end{align*}
\end{itemize}

\section{Formulas and so on}

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aliquam, integer placerat et turpis mi eros nec lobortis taciti, vehicula
nisl litora tellus ligula porttitor metus. Vivamus integer non suscipit
taciti mus etiam at primis tempor sagittis sit, euismod libero facilisi
aptent elementum felis blandit cursus gravida sociis erat ante, eleifend
lectus nullam dapibus netus feugiat curae curabitur est ad. Massa
curae fringilla porttitor quam sollicitudin iaculis aptent leo ligula
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mauris eros etiam praesent erat volutpat posuere hac. Metus fringilla
nec ullamcorper odio aliquam lacinia conubia mauris tempor, etiam
ultricies proin quisque lectus sociis id tristique, integer phasellus
taciti pretium adipiscing tortor sagittis ligula. Mollis pretium lorem
primis senectus habitasse lectus scelerisque donec, ultricies tortor
suspendisse adipiscing fusce morbi volutpat pellentesque, consectetur
mi risus molestie curae malesuada cum. Dignissim lacus convallis massa
mauris enim ad mattis magnis senectus montes, mollis taciti phasellus
accumsan bibendum semper blandit suspendisse faucibus nibh est, metus
lobortis morbi cras magna vivamus per risus fermentum. Dapibus imperdiet
praesent magnis ridiculus congue gravida curabitur dictum sagittis,
enim et magna sit inceptos sodales parturient pharetra mollis, aenean
vel nostra tellus commodo pretium sapien sociosqu.

Lorem ipsum dolor sit amet consectetur adipiscing elit, urna consequat
felis vehicula class ultricies mollis dictumst, aenean non a in donec
nulla. Phasellus ante pellentesque erat cum risus consequat imperdiet
aliquam, integer placerat et turpis mi eros nec lobortis taciti, vehicula
nisl litora tellus ligula porttitor metus. Vivamus integer non suscipit
taciti mus etiam at primis tempor sagittis sit, euismod libero facilisi
aptent elementum felis blandit cursus gravida sociis erat ante, eleifend
lectus nullam dapibus netus feugiat curae curabitur est ad. Massa
curae fringilla porttitor quam sollicitudin iaculis aptent leo ligula
euismod dictumst, orci\footnote{This is actually non-sense.} penatibus
mauris eros etiam praesent erat volutpat posuere hac. Metus fringilla
nec ullamcorper odio aliquam lacinia conubia mauris tempor, etiam
ultricies proin quisque lectus sociis id tristique, integer phasellus
taciti pretium adipiscing tortor sagittis ligula. Mollis pretium lorem
primis senectus habitasse lectus scelerisque donec, ultricies tortor
suspendisse adipiscing fusce morbi volutpat pellentesque, consectetur
mi risus molestie curae malesuada cum. Dignissim lacus convallis massa
mauris enim ad mattis magnis senectus montes, mollis taciti phasellus
accumsan bibendum semper blandit suspendisse faucibus nibh est, metus
lobortis morbi cras magna vivamus per risus fermentum. Dapibus imperdiet
praesent magnis ridiculus congue gravida curabitur dictum sagittis,
enim et magna sit inceptos sodales parturient pharetra mollis, aenean
vel nostra tellus commodo pretium sapien sociosqu.

Lorem ipsum dolor sit amet consectetur adipiscing elit, urna consequat
felis vehicula class ultricies mollis dictumst, aenean non a in donec
nulla. Phasellus ante pellentesque erat cum risus consequat imperdiet
aliquam, integer placerat et turpis mi eros nec lobortis taciti, vehicula
nisl litora tellus ligula porttitor metus. Vivamus integer non suscipit
taciti mus etiam at primis tempor sagittis sit, euismod libero facilisi
aptent elementum felis blandit cursus gravida sociis erat ante, eleifend
lectus nullam dapibus netus feugiat curae curabitur est ad. Massa
curae fringilla porttitor quam sollicitudin iaculis aptent leo ligula
euismod dictumst, orci\footnote{This is actually non-sense.} penatibus
mauris eros etiam praesent erat volutpat posuere hac. Metus fringilla
nec ullamcorper odio aliquam lacinia conubia mauris tempor, etiam
ultricies proin quisque lectus sociis id tristique, integer phasellus
taciti pretium adipiscing tortor sagittis ligula. Mollis pretium lorem
primis senectus habitasse lectus scelerisque donec, ultricies tortor
suspendisse adipiscing fusce morbi volutpat pellentesque, consectetur
mi risus molestie curae malesuada cum. Dignissim lacus convallis massa
mauris enim ad mattis magnis senectus montes, mollis taciti phasellus
accumsan bibendum semper blandit suspendisse faucibus nibh est, metus
lobortis morbi cras magna vivamus per risus fermentum. Dapibus imperdiet
praesent magnis ridiculus congue gravida curabitur dictum sagittis,
enim et magna sit inceptos sodales parturient pharetra mollis, aenean
vel nostra tellus commodo pretium sapien sociosqu.

Lorem ipsum dolor sit amet consectetur adipiscing elit, urna consequat
felis vehicula class ultricies mollis dictumst, aenean non a in donec
nulla. Phasellus ante pellentesque erat cum risus consequat imperdiet
aliquam, integer placerat et turpis mi eros nec lobortis taciti, vehicula
nisl litora tellus ligula porttitor metus. Vivamus integer non suscipit
taciti mus etiam at primis tempor sagittis sit, euismod libero facilisi
aptent elementum felis blandit cursus gravida sociis erat ante, eleifend
lectus nullam dapibus netus feugiat curae curabitur est ad. Massa
curae fringilla porttitor quam sollicitudin iaculis aptent leo ligula
euismod dictumst, orci\footnote{This is actually non-sense.} penatibus
mauris eros etiam praesent erat volutpat posuere hac. Metus fringilla
nec ullamcorper odio aliquam lacinia conubia mauris tempor, etiam
ultricies proin quisque lectus sociis id tristique, integer phasellus
taciti pretium adipiscing tortor sagittis ligula. Mollis pretium lorem
primis senectus habitasse lectus scelerisque donec, ultricies tortor
suspendisse adipiscing fusce morbi volutpat pellentesque, consectetur
mi risus molestie curae malesuada cum. Dignissim lacus convallis massa
mauris enim ad mattis magnis senectus montes, mollis taciti phasellus
accumsan bibendum semper blandit suspendisse faucibus nibh est, metus
lobortis morbi cras magna vivamus per risus fermentum. Dapibus imperdiet
praesent magnis ridiculus congue gravida curabitur dictum sagittis,
enim et magna sit inceptos sodales parturient pharetra mollis, aenean
vel nostra tellus commodo pretium sapien sociosqu.
\end{document}