density est

notes/11_density-est/1_kde.tex

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+\begin{frame}
+\end{frame}
+
+\begin{frame}
+
+\section{Density Estimation: What and Why?}
+\notesonly{
+We observe data. 
+This data is generated by some unknown probability distribution. Each observation is a sample from this distrubtion.
+When we talk about density estimation, we are talking about recovering the underlying probability density function that produced te observed samples.
+}
+
+\question{Why do we care about estimating densities? What can we do with an estimated density?}
+
+\begin{itemize}
+\item data exploration
+\item visualization (for 1D and 2D data)
+\item deduce moments (mean, variance, \ldots)
+\item describe the data in compact form (e.g. this data follows a Gaussian with mean $\mu$ and covariance $\vec \Sigma$)
+\item generate new data
+\item unsupervised anomaly detection
+\end{itemize}
+
+\end{frame}
+
+\begin{frame}
+
+\underline{Density Estimation: How?}
+
+2 strategies:
+
+\begin{enumerate}[(A)]
+\item \textbf{parametric} methods:
+\\ We assume that the data follows some class of distribution and we estimate its paramters (e.g. fit a Gaussian around this data)
+\item \textbf{non-parametric}\footnote{non-parametric does not means it is void of paramters. 
+It is just that the parameters do not directly correspond to the classical parameters of densities such as mean and variance.} methods: 
+data-driven. Estimate the density with as few assumptions as possible (e.g. Kernel\footnote{Not tied to Mercer Kernels like in Kernel PCA. A kernel is just some non-negative function.} density estimation)
+\end{enumerate}
+
+\end{frame}
+
+Many people habe already encountered density estimation in the form of histograms.
+
+\begin{frame}
+\end{frame}
+
+\begin{frame}
+
+\begin{figure}[ht]
+     \centering
+     \savebox{\imagebox}{\includegraphics[width=0.4\textwidth]{img/spiral_data.png}}%
+     \begin{subfigure}[t]{0.4\textwidth}
+         \centering
+         \usebox{\imagebox}% Place largest image
+         \caption{original observations $\vec x$}
+         \label{fig:spiral_data}
+     \end{subfigure}
+     \hfill
+     \begin{subfigure}[t]{0.35\textwidth}
+         \centering
+         \raisebox{\dimexpr.5\ht\imagebox-.5\height}{% Raise smaller image into place
+         \includegraphics[width=\textwidth]{img/spiral_pca.png}
+         }
+         \caption{projection onto the first 2 PCs}
+         \label{fig:spiral_pca}
+     \end{subfigure}
+     \caption{Dimensionality reduction of ``spiral data''. Points are colored according to their index in the dataset.}
+	 \label{fig:spiral}
+\end{figure}
+
+\end{frame}
+

notes/11_density-est/Makefile

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+all: slides notes clean
+#all:  handout
+
+projname = tutorial
+targetname = $(projname)_$(shell basename $(CURDIR))
+compile = pdflatex
+projnameS = $(projname).slides
+projnameH = $(projname).handout
+projnameA = $(projname).notes
+
+slides: $(projname).slides.tex $(projname).tex
+	$(compile) $(projname).slides.tex
+#	bibtex $(projname).slides
+#	$(compile) --interaction=batchmode  $(projname).slides.tex
+#	$(compile) --interaction=batchmode  $(projname).slides.tex
+	mv $(projname).slides.pdf $(targetname).slides.pdf 
+
+handout: $(projname).handout.tex $(projname).tex
+	$(compile) $(projname).handout.tex
+	mv $(projname).handout.pdf $(targetname).handout.pdf 
+
+# Repeat compilation for the references to show up correctly
+notes: $(projname).notes.tex $(projname).tex
+	$(compile) $(projname).notes.tex
+#	bibtex $(projname).notes
+#	$(compile) --interaction=batchmode  $(projname).notes.tex
+	$(compile) --interaction=batchmode  $(projname).notes.tex
+	mv $(projname).notes.pdf $(targetname).notes.pdf 
+
+clean: cleans cleanh cleana
+
+cleans:
+	rm -f $(projnameS).aux $(projnameS).bbl $(projnameS).log $(projnameS).out $(projnameS).toc $(projnameS).lof $(projnameS).glo $(projnameS).glsdefs $(projnameS).idx $(projnameS).ilg $(projnameS).ind $(projnameS).loa $(projnameS).lot $(projnameS).loe $(projnameS).snm $(projnameS).nav
+
+cleanh:
+	rm -f $(projnameH).aux $(projnameH).bbl $(projnameH).log $(projnameH).out $(projnameH).toc $(projnameH).lof $(projnameH).glo $(projnameH).glsdefs $(projnameH).idx $(projnameH).ilg $(projnameH).ind $(projnameH).loa $(projnameH).lot $(projnameH).loe $(projnameH).snm $(projnameH).nav
+
+cleana:	
+	rm -f $(projnameA).aux $(projnameA).bbl $(projnameA).log $(projnameA).out $(projnameA).toc $(projnameA).lof $(projnameA).glo $(projnameA).glsdefs $(projnameA).idx $(projnameA).ilg $(projnameA).ind $(projnameA).loa $(projnameA).lot $(projnameA).loe $(projnameA).snm $(projnameA).nav
+

notes/11_density-est/beamercolorthemetub.sty

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+% Copyright 2004 by Madhusudan Singh <[email protected]>
+%
+% This file may be distributed and/or modified
+%
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Public License.
+%
+% See the file doc/licenses/LICENSE for more details.
+
+%\ProvidesPackageRCS $Header: beamercolorthemetub.sty, v a01 2011/11/18 09:11:41 tujl $
+
+\mode<presentation>
+
+\definecolor{darkred}{rgb}{0.8,0,0}
+
+\setbeamercolor{section in toc}{fg=black,bg=white}
+\setbeamercolor{alerted text}{fg=darkred!80!gray}
+
+\setbeamercolor*{palette primary}{fg=darkred!60!black,bg=gray!30!white}
+\setbeamercolor*{palette secondary}{fg=darkred!70!black,bg=gray!15!white}
+\setbeamercolor*{palette tertiary}{bg=darkred!80!black,fg=gray!10!white}
+\setbeamercolor*{palette quaternary}{fg=darkred,bg=gray!5!white}
+
+\setbeamercolor*{sidebar}{fg=darkred,bg=gray!15!white}
+
+\setbeamercolor*{palette sidebar primary}{fg=darkred!15!black}
+\setbeamercolor*{palette sidebar secondary}{fg=white}
+\setbeamercolor*{palette sidebar tertiary}{fg=darkred!50!black}
+\setbeamercolor*{palette sidebar quaternary}{fg=gray!15!white}
+
+%\setbeamercolor*{titlelike}{parent=palette primary}
+\setbeamercolor{titlelike}{parent=palette primary,fg=darkred}
+\setbeamercolor{frametitle}{bg=gray!15!white}
+\setbeamercolor{frametitle right}{bg=gray!60!white}
+
+%\setbeamercolor{Beispiel title}{bg=white,fg=black}
+
+\setbeamercolor*{separation line}{}
+\setbeamercolor*{fine separation line}{}
+
+%\setbeamercolor{itemize item}{fg=darkred,bg=white}
+%\setbeamercolor{itemize subitem}{fg=darkred!60!white,bg=white}
+%\setbeamercolor{local structure}{fg=darkred,bg=white}
+\setbeamercolor{local structure}{fg=gray,bg=white}
+\setbeamercolor{structure}{fg=darkred!80!black,bg=white}
+\setbeamercolor{block title}{bg=gray!10!white}
+\mode
+<all>

notes/11_density-est/beamerthemeTUBerlin.sty

@@ -0,0 +1,22 @@
+% Copyright 2004 by Madhusudan Singh <[email protected]>
+%
+% This file may be distributed and/or modified
+%
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Public License.
+%
+% See the file doc/licenses/LICENSE for more details.
+
+%\ProvidesPackageRCS $Header: beamerthemeTUBerlin.sty, v a01 2011/11/18 09:11:41 tujl $
+\mode<presentation>
+
+\useinnertheme[shadow=true]{rounded}
+\useoutertheme{infolines}
+\usecolortheme{tub}
+
+\setbeamerfont{frametitle}{size=\normalsize}
+\setbeamerfont{block title}{size={}}
+%\setbeamerfont{structure}{series=\bfseries}
+\setbeamercolor{titlelike}{parent=structure,bg=white}
+\mode
+<all>

notes/11_density-est/bibliography.bib

@@ -0,0 +1,29 @@
+@book{sutton1998introduction,
+  title={Introduction to reinforcement learning},
+  author={Sutton, Richard S and Barto, Andrew G and others},
+  volume={135},
+  year={1998},
+  publisher={MIT press Cambridge}
+}
+@Book{Bertsekas07,
+  author = 	 {D. P. Bertsekas},
+  title = 	 {Dynamic Programming and Optimal Control},
+  publisher ={Athena Scientific},
+  year = 	 {2007},
+  volume = 	 {2},
+  edition =  {3rd},
+  url = {http://www.control.ece.ntua.gr/UndergraduateCourses/ProxTexnSAE/Bertsekas.pdf}
+}
+@Article{Watkins92,
+  author = 	 {C. Watkins and P. Dayan},
+  title = 	 {Q-learning},
+  journal = 	 {Machine Learning},
+  year = 	 {1992},
+  OPTkey = 	 {},
+  volume = 	 {8},
+  OPTnumber = 	 {},
+  pages = 	 {279--292},
+  OPTmonth = 	 {},
+  OPTnote = 	 {},
+  OPTannote = 	 {}
+}

notes/11_density-est/tutorial.handout.tex

@@ -0,0 +1,14 @@
+\documentclass[handout,ignorenonframetext]{beamer} 
+\newcounter{baslide}
+\setcounter{baslide}{1}
+
+\let\oldframe
+\frame                                                             
+\let\oldendframe
+\endframe
+
+\def\frame{\oldframe \label{baslide\roman{baslide}}%
+\addtocounter{baslide}{1}}  
+\def\endframe{\oldendframe}
+
+\input{tutorial}

notes/11_density-est/tutorial.notes.tex

@@ -0,0 +1,17 @@
+\documentclass{../../latex/minotes}
+\input{../../latex/customcommands}
+
+\numberwithin{equation}{section}
+\numberwithin{figure}{section}
+
+\let\oldframe\frame
+\let\oldendframe\endframe
+
+\newcommand{\notesonly}[1]{#1}
+
+\newcommand{\mystackrel}[2]{\stackrel{\mathmakebox[\widthof{#1}]{#2}}{=}}
+
+% frame titles only effective in presentation mode
+\renewcommand{\frametitle}[1]{}
+
+\input{tutorial}

notes/11_density-est/tutorial.slides.tex

@@ -0,0 +1,11 @@
+\input{../../latex/headerMIslides}
+\input{../../latex/customcommands}
+
+\subtitle{1.1 Intro \& 1.2 Connectionist Neuron}
+\mathtoolsset{showonlyrefs}
+
+\newcommand{\slidesonly}[1]{#1}
+
+\newcommand{\mystackrel}[2]{\stackrel{\mathmakebox[\widthof{#1}]{#2}}{=}}
+
+\input{tutorial}

notes/11_density-est/tutorial.tex

@@ -0,0 +1,80 @@
+\usepackage[authoryear,round]{natbib}
+\usepackage{multirow}
+
+\newcommand{\sheetnum}{%
+	11
+}
+%\setcounter{section}{\sheetnum-3}
+\newcommand{\tutorialtitle}{%
+    Density Estimation and Estimation bias
+}
+\newcommand{\tutorialtitleshort}{%
+	Density Estimation
+}
+% for slides
+\subtitle{\sheetnum \tutorialtitle}
+
+%\maxdeadcycles=1000 % Workaround for ! Output loop---100 consecutive dead cycles because of too many figures
+
+% The following use of algroithms does not work well with the notes:
+%
+%
+%
+%
+% instead use the following for your algorithms:
+%
+%\begin{figure}[!t]
+%\removelatexerror
+%\begin{algorithm}[H]
+    % your algo here
+    %\label{alg:algolabel}
+    %\caption{algocaption}
+%\end{algorithm}
+%\end{figure}
+%\begin{algorithm}
+% Below is the definition for the command \removelatexerror:
+\makeatletter
+\newcommand{\removelatexerror}{\let\@latex@error\@gobble}
+\makeatother
+
+\begin{document} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\sheet{\sheetnum}{\tutorialtitleshort}
+
+\ttopic{\tutorialtitle}
+
+\columnratio{0.2,0.8}\textbf{}
+\begin{paracol}{2}
+%\setlength{\columnseprule}{0.1pt}
+%\setlength{\columnsep}{5em}
+
+\begin{rightcolumn}
+
+% notes version will ignore it
+\begin{frame}
+\titlepage
+\end{frame}
+
+\begin{frame}
+\tableofcontents
+\end{frame}
+
+\newpage
+
+\mode<all>
+\input{./1_kde}
+\mode*
+
+\clearpage
+
+%\section{References}
+%\begin{frame}[allowframebreaks] \frametitle{References}
+	%\scriptsize
+	%\bibliographystyle{plainnat}
+	%\bibliography{bibliography}
+%\end{frame}
+
+\end{rightcolumn}
+\end{paracol}
+
+\end{document}