preamble.tex

%% Pre-amble - commonly defined macros.

%% Packages
\usepackage{fixltx2e}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{isomath}
\usepackage{amsthm}
\usepackage{dsfont}
%%\usepackage{theorem}
\usepackage{algorithm}
\usepackage{algorithmicx}
\usepackage{algpseudocode}
\usepackage{mathrsfs}
\usepackage{epsfig}
\usepackage{subcaption}
\usepackage{makeidx} 
\usepackage{colortbl}
\usepackage{enumerate}
\usepackage{multirow}
\usepackage{listings}
\usepackage{pgfplots}
\usepackage{fontawesome}
\newlength\fheight
\newlength\fwidth
\only<presentation>{
\setlength\fheight{\textheight}
\setlength\fwidth{0.45\columnwidth}
}
\only<article>{
\setlength\fheight{0.25\textheight}
\setlength\fwidth{0.45\textwidth}
}
\usepackage[sort&compress,comma,super]{natbib}
\def\newblock{} % To avoid a compilation error about a function \newblock undefined
\usepackage{hyperref}

\newcommand \cdcomment[1] {\texttt{\color{red}[CD: #1]}}
  
\setbeamertemplate{theorems}[numbered] 
\mode<presentation>{
\theoremstyle{plain}
\newtheorem{assumption}{Assumption}
\theoremstyle{definition}
\newtheorem{exercise}{Exercise}
\theoremstyle{remark}
\newtheorem{remark}{Remark}
}

\numberwithin{equation}{section} 
\mode<article>{
  \theoremstyle{plain}
  % \newtheorem{assumption}{Assumption}[section]
  \newtheorem{lemma}{Lemma}[section]
  \newtheorem{theorem}{Theorem}[section]
  \newtheorem{corollary}{Corollary}[section]
  \theoremstyle{definition}
  \newtheorem{definition}{Definition}[section]
  \theoremstyle{remark}
  \newtheorem{remark}{Remark}[section]

  % \theoremstyle{plain} \newtheorem{remark}{Remark}[section]
  % \theoremstyle{plain} \newtheorem{definition}{Definition}[section]
  \theoremstyle{plain} \newtheorem{assumption}{Assumption}[section]
  
  %%% Examples %%%%
  \newtheoremstyle{example}  % Name
  {1em}       % Space above 
  {1em}       % Space below
  {\small}      % Body font
  {}          % Indent amount 
  {\scshape}  % Theorem head font
  {.}         % Punctuation after theorem head
  {.5em}      % Space after theorem head
  {}          % Theorem head spec
  \theoremstyle{example}
  \newtheorem{example}{Example}
  \newtheorem{exercise}{Exercise}

  \usepackage{framed}
  \usepackage[framemethod=tikz]{mdframed}
  \mdfsetup{%
    roundcorner=10pt}
  \renewenvironment{block}[1]
  {\begin{mdframed}[frametitle={#1}]}
    {\end{mdframed}}

  \renewenvironment{exampleblock}[1]
  {\begin{mdframed}[frametitle={\faGears{} #1}]}
    {\end{mdframed}}


  \renewenvironment{alertblock}[1]
  {\begin{mdframed}[backgroundcolor=red!20,frametitle={{\fontencoding{U}\fontfamily{futs}\selectfont\char 66\relax} #1}]}
    {\end{mdframed}}


  \newenvironment{theoryblock}[1]
  {\begin{mdframed}[backgroundcolor=yellow!20,frametitle={\Coffeecup #1}]}
    {\end{mdframed}}

  \newenvironment{exerciseblock}[1]
  {\begin{mdframed}[backgroundcolor=blue!10,frametitle={\faPencilSquareO{} #1}]}
    {\end{mdframed}}

  \newenvironment{groupactivity}[1]
  {\begin{mdframed}[backgroundcolor=cyan!20,frametitle={\faGroup{} #1}]}
    {\end{mdframed}}

  
}
%\theoremstyle{plain} \newtheorem{conjecture}{Conjecture}[section]
%\theoremstyle{plain} \newtheorem{theorem}{Theorem}[section]
%\theoremstyle{plain} \newtheorem{proposition}{Proposition}[section]
%\theoremstyle{plain} \newtheorem{lemma}{Lemma}[section]
%\theoremstyle{plain} \newtheorem{corollary}{Corollary}[section]


%\newenvironment{proof}[1][Proof]{\begin{trivlist}
%\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
%\newcommand{\qed}{\nobreak \ifvmode \relax \else
%      \ifdim\lastskip<1.5em \hskip-\lastskip
%      \hskip1.5em plus0em minus0.5em \fi \nobreak
%      \vrule height0.5em width0.5em depth0.25em\fi}

\newcommand \indexmargin[1] {\marginpar{\emph{#1}}\index{#1}}
\newcommand \marginref[2] {\marginpar{\emph{#1}}\emph{#1}\index{#2}}
\newcommand \emindex[1] {\emph{#1}\marginpar{\emph{#1}}\index{#1}}


\newcommand \E {\mathop{\mbox{\ensuremath{\mathbb{E}}}}\nolimits}
\newcommand \hE {\hat{\mathop{\mbox{\ensuremath{\mathbb{E}}}}\nolimits}}
\renewcommand \Pr {\mathop{\mbox{\ensuremath{\mathbb{P}}}}\nolimits}
\newcommand \given {\mathrel{|}}
\newcommand \gvn {|}
\newcommand \eq {{=}}


%% Special characters
\newcommand\Reals {{\mathbb{R}}}
\newcommand\Naturals {{\mathbb{N}}} 
\newcommand\Simplex {\mathbold{\Delta}}

\newcommand \FB {{\mathfrak{B}}}
\newcommand \FD {{\mathfrak{D}}}
\newcommand \FF {{\mathfrak{F}}}
\newcommand \FM {{\mathfrak{M}}}
\newcommand \FK {{\mathfrak{K}}}
\newcommand \FJ {{\mathfrak{J}}}
\newcommand \FL {{\mathfrak{L}}}
\newcommand \FO {{\mathfrak{O}}}
\newcommand \FS {{\mathfrak{S}}}
\newcommand \FT {{\mathfrak{T}}}
\newcommand \FP {{\mathfrak{P}}}
\newcommand \FR {{\mathfrak{R}}}


\newcommand \CA {{\mathcal{A}}}
\newcommand \CB {{\mathcal{B}}}
\newcommand \CC {{\mathcal{C}}}
\newcommand \CD {{\mathcal{D}}}
\newcommand \CE {{\mathcal{E}}}
\newcommand \CF {{\mathcal{F}}}
\newcommand \CG {{\mathcal{G}}}
\newcommand \CH {{\mathcal{H}}}
\newcommand \CJ {{\mathcal{J}}}
\newcommand \CL {{\mathcal{L}}}
\newcommand \CM {{\mathcal{M}}}
\newcommand \CN {{\mathcal{N}}}
\newcommand \CO {{\mathcal{O}}}
\newcommand \CP {{\mathcal{P}}}
\newcommand \CQ {{\mathcal{Q}}}
\newcommand \CR {{\mathcal{R}}}
\newcommand \CS {{\mathcal{S}}}
\newcommand \CT {{\mathcal{T}}}
\newcommand \CU {{\mathcal{U}}}
\newcommand \CV {{\mathcal{V}}}
\newcommand \CW {{\mathcal{W}}}
\newcommand \CX {{\mathcal{X}}}
\newcommand \CY {{\mathcal{Y}}}
\newcommand \CZ {{\mathcal{Z}}}

\newcommand \BA {{\mathbb{A}}}
\newcommand \BI {{\mathbb{I}}}
\newcommand \BS {{\mathbb{S}}}

\newcommand \bx {{\vectorsym{x}}}
\newcommand \by {{\vectorsym{y}}}
\newcommand \bu {{\vectorsym{u}}}
\newcommand \bw {{\vectorsym{w}}}
\newcommand \ba {{\vectorsym{a}}}
\newcommand \bc {{\vectorsym{c}}}
\newcommand \bz {{\vectorsym{z}}}
\newcommand \bq {{\vectorsym{q}}}
\newcommand \bat {{\vectorsym{a}_t}}
\newcommand \bh {{\vectorsym{h}}}
\newcommand \bo {{\vectorsym{o}}}
\newcommand \bp {{\vectorsym{p}}}
\newcommand \bs {{\vectorsym{s}}}
\newcommand \br {{\vectorsym{r}}}

\newcommand \SA {\mathscr{A}}
\newcommand \SB {\mathscr{B}}
\newcommand \SC {\mathscr{C}}
\newcommand \SF {\mathscr{F}}
\newcommand \SG {\mathscr{G}}
\newcommand \SH {\mathscr{H}}
\newcommand \SJ {\mathscr{J}}
\newcommand \SL {\mathscr{L}}
\newcommand \SP {\mathscr{P}}
\newcommand \SR {\mathscr{R}}
%%\newcommand \SS {\mathscr{S}}
\newcommand \ST {\mathscr{T}}
\newcommand \SU {\mathscr{U}}
\newcommand \SV {\mathscr{V}}
\newcommand \SW {\mathscr{W}}

\newcommand \hM {\widehat{M}}

\newcommand \KL[2] {\mathbb{D}\left( #1 \| #2 \right)}


%\newcommand \p {\partial}

\newcommand \then{\Rightarrow}
\newcommand \defn {\mathrel{\triangleq}}
\newcommand \st {\mathop{\rm s.t.}}
%\newcommand \StateSet {{\CQ}}


%% Commands

\newcommand \argmax{\mathop{\rm arg\,max}}
\newcommand \argmin{\mathop{\rm arg\,min}}
\newcommand \dtan{\mathop{\rm dtan}}
\newcommand \sgn{\mathop{\rm sgn}}
\newcommand \trace{\mathop{\rm tr}}

\newcommand \onenorm[1]{\left\|#1\right\|_1}
\newcommand \pnorm[2]{\left\|#1\right\|_{#2}}
\newcommand \inftynorm[1]{\left\right\|#1\|_\infty}
\newcommand \norm[1]{\left\|#1\right\|}

%%\newcommand \defn {\triangleq}
%%\newcommand \defn {\equiv}
%%\newcommand \defn {\coloneq}
%%\newcommand \defn {\stackrel{\text{\tiny def}}{=}}
%%\newcommand \defn {\stackrel{\text{def}}{\hbox{\equalsfill}}}

\DeclareMathAlphabet{\mathpzc}{OT1}{pzc}{m}{it}

\newcommand \Normal {\mathop{\mathpzc{N}}\nolimits}
\newcommand \Poisson {\mathop{\mathpzc{Poisson}}\nolimits}
\newcommand \Multinomial {\mathop{\mathpzc{Multinomial}}\nolimits}
\newcommand \Dirichlet {\mathop{\mathpzc{Dirichlet}}\nolimits}
\newcommand \Student {\mathop{\mathpzc{Student}}\nolimits}
\newcommand \Bernoulli {\mathop{\mathpzc{Bernoulli}}\nolimits}
\newcommand \BetaDist   {\mathop{\mathpzc{Beta}}\nolimits}
\newcommand \Singular   {\mathop{\mathpzc{D}}\nolimits}
\newcommand \GammaDist {\mathop{\mathpzc{Gamma}}\nolimits}
\newcommand \Softmax{\mathop{\mathpzc{Softmax}}\nolimits}
\newcommand \Exp{\mathop{\mathpzc{Exp}}\nolimits}
\newcommand \Uniform{\mathop{\mathpzc{Unif}}\nolimits}
\newcommand \Laplace {\mathop{\mathpzc{Laplace}}\nolimits}

\newcommand \Param {\Theta}
\newcommand \param {\theta}
\newcommand \vparam {\vectorsym{\theta}}
\newcommand \mparam {\matrixsym{\Theta}}
\newcommand \Hyperparam {\Phi}
\newcommand \hyperparam {\phi}
\newcommand \family {\mathcal{F}}
\newcommand{\ie}{\emph{i.e.}~}
\newcommand{\eg}{\emph{e.g.}~}
\newcommand{\etal}{\emph{et al.}~}
\newcommand{\constg}{}
\newcommand{\Bel}{\mathcal{B}}
\newcommand \Bay {\ensuremath{\mathscr{B}}}
\newcommand \Adv {\ensuremath{\mathscr{A}}}

\newcommand \step {\eta}

\newcommand \Borel[1] {\FF(#1)}
\newcommand \Probs[1] {\FM(#1)}


\newcommand \pol {\pi}
\newcommand \Pol {\Pi}
\newcommand \mdp {\mu}
\newcommand \MDP {\CM}
\newcommand \meanMDP {{\bar{\mdp}_\xi}}

\newcommand {\msqr} {\vrule height0.33cm width0.44cm}
\newcommand {\bsqr} {\vrule height0.55cm width0.66cm}

\newcommand\ind[1]{\mathop{\mbox{\ensuremath{\mathbb{I}}}}\left\{#1\right\}}
\newcommand\Ind{\mbox{\bf{I}}}

\newcommand\dd{\,\mathrm{d}}

\newcommand \seq[2]{#1^{#2}}
\newcommand \pseq[3]{#1_{#2}^{#3}}
\newcommand \sam[2]{#1^{(#2)}}
\newcommand \transpose[1] {#1^\top}
\newcommand\set[1] {\left\{#1\right\}}
\newcommand\tuple[1] {\left\langle #1\right\rangle}
\newcommand\cset[2] {\left\{#1 ~\middle|~ #2\right\}}
\newcommand \ceil[1]{\left\lceil #1 \right\rceil}





\newcommand{\indep}{\mathrel{\text{\scalebox{1.07}{$\perp\mkern-10mu\perp$}}}}


\newcommand \eqlike {\eqsim}
\newcommand \gtlike {\succ}
\newcommand \ltlike {\prec}
\newcommand \gelike {\succsim}
\newcommand \lelike {\precsim}

\newcommand \eqpref {\eqsim^*}
\newcommand \gtpref {\succ^*}
\newcommand \ltpref {\prec^*}
\newcommand \gepref {\succsim^*}
\newcommand \lepref {\precsim^*}

\newcommand \util {U}
\newcommand \BUtil {U^*}
\newcommand \MUtil {\matrixsym{U}}
\newcommand \risk {\sigma}
\newcommand \Brisk {\sigma^*}
\newcommand \Loss {\ell}
\newcommand \Regret {L}
\newcommand \regret {\ell}
\newcommand \Reward {\SR}
\newcommand \reward {r}
\newcommand \vreward {\vectorsym{r}}
\newcommand \Rew {\rho}
\newcommand \boutcome {\vectorsym{\omega}}
\newcommand \outcome {\omega}
\newcommand \Outcome {\Omega}
\newcommand \act {a}
\newcommand \Act {\CA}
\newcommand \decision {a}
\newcommand \Decision {\mathcal{A}}
\newcommand \dec {\delta}
\newcommand \Dec {\mathscr{D}}


\newcommand {\MH} {\matrixsym{H}}

\newcommand \alg {\lambda}
\newcommand \Alg {\Lambda}
\newcommand \KNN {\textsc{k-NN}}

\newcommand \model {\mu}
\newcommand \MAP {\model_{\textrm{MAP}}}
\newcommand \Model {\CM}
\newcommand \Datasets {\CD}
\newcommand \Data {D}
\newcommand \Training {D_T}
\newcommand \Holdout {D_H}
\newcommand \Testing {D^*}
\newcommand \error {\epsilon}
\newcommand \obs {x}
\newcommand \Obs {\CX}
\newcommand \Att {\CA}
\newcommand \att {a}
\newcommand \attv {v}
\newcommand \Attv {\CV}
\newcommand \cls {y}
\newcommand \Cls {\CY}
\newcommand \Entropy {\mathbb{H}}
\newcommand \Gain {\mathbb{G}}

\newcommand {\neigh} {\simeq}
\newcommand \hock[3] {\chi_{#1}\left(#2 \middle\| #3 \right)}
\newcommand \renyi[3] {D_{#1}\left(#2 \middle\| #3 \right)}

\newcommand \IDThree {\texttt{ID3}}

\newcommand \nactions {A}
\newcommand \nclasses {C}
\newcommand \nstates{S}
\newcommand \nobservations {N}
\newcommand \ndata{T}

\newcommand \figwidth {0.6\textwidth}
\newcommand \figheight {0.4\textwidth}

\newcommand \eye {\matrixsym{I}}
\newcommand \MA {\matrixsym{A}}
\newcommand \MC {\matrixsym{C}}
\newcommand \MX {\matrixsym{X}}
\newcommand \MR {\matrixsym{R}}
\newcommand \MY {\matrixsym{Y}}
\newcommand \MB {\matrixsym{B}}
\newcommand \MV {\matrixsym{V}}
\newcommand \MW {\matrixsym{W}}
\newcommand \MP {\matrixsym{P}}
\newcommand \MZ {\matrixsym{Z}}

\newcommand \vg {\vectorsym{\gamma}}
\newcommand \vp {\vectorsym{p}}
\newcommand \vs {\vectorsym{s}}
\newcommand \vx {\vectorsym{x}}
\newcommand \vr {\vectorsym{r}}
\newcommand \vm {\vectorsym{m}}
\newcommand \vb {\vectorsym{b}}
\newcommand \vt {\vectorsym{\theta}}

\newcommand \pn[1] {\vx_{[#1]}}

\newcommand \basis {f}
\newcommand \bel {\beta}
\newcommand \hyper {\omega}
\newcommand \mbel {\bel^D}
\newcommand \pbel {\bel^C}

\newcommand \pmean {\matrixsym{M}}
\newcommand \pcov {\matrixsym{C}}
\newcommand \pwish {\matrixsym{W}}
\newcommand \porder {n}

\newcommand \Syx {\matrixsym{\Sigma}_{yx}}
\newcommand \Sxx {\matrixsym{\Sigma}_{xx}}
\newcommand \Syy {\matrixsym{\Sigma}_{yy}}
\newcommand \Symx {\matrixsym{\Sigma}_{y\mid x}}

\newcommand \trans {\matrixsym{P}}
\newcommand \ident {\matrixsym{I}}

\newcommand \noise {\vectorsym{\varepsilon}}

\newcommand \pt {p_t}


\newcommand \CSet {G}
\newcommand \Parent[1] {\mathfrak{P}(#1)}
\newcommand \Children[1] {\mathfrak{C}(#1)}
\newcommand \Ancestors[1] {\mathfrak{A}(#1)}
\newcommand \Descendants[1] {\mathfrak{D}(#1)}
\newcommand \metric[2] {\nu(#1, #2)}
\newcommand \zooming {\zeta}
\newcommand \depth[1] {d(#1)}

\newcommand \sensitivity[1] {\mathbb{L}\left(#1\right)}
\newcommand \disc {\gamma}
\newcommand \Value {V}
\newcommand \val {\vectorsym{v}}
\newcommand \Vals {\mathcal{V}}
\newcommand \qval {\vectorsym{q}}
\newcommand \Qvals {\mathcal{Q}}
\newcommand \blm {\mathscr{L}}
\newcommand \tdm {\mathscr{D}}
\newcommand \pim {\mathscr{B}}



\newcommand \dist[2]{D\left(#1 ~\middle\|~ #2\right)}

\newcommand \Ae {A_\epsilon^\hist}

\newcommand \lrdist[2]{d_{lr}(#1, #2)}
\newcommand \xdistChar{\rho}
\newcommand \xdist[2]{\xdistChar(#1, #2)}
\newcommand \pdist[2]{\kappa(#1, #2)}
\newcommand{\constScale}{\omega}
\newcommand{\constScaleB}{\kappa}

\newcommand \fields[1]{\sigma(#1)}

\newcommand \hist {h}

\newcommand \abs[1] {\left|#1\right|}

\newcommand{\errorband}[5][]{ % x column, y column, error column, optional argument for setting style of the area plot
\pgfplotstableread[col sep=comma, skip first n=2]{#2}\datatable
% Lower bound (invisible plot)
\addplot [draw=none, stack plots=y, forget plot] table [
x={#3},
y expr=\thisrow{#4}-\thisrow{#5}
] {\datatable};

% Stack twice the error, draw as area plot
\addplot [draw=none, fill=gray!40, stack plots=y, area legend, #1] table [
x={#3},
y expr=2*\thisrow{#5}
] {\datatable} \closedcycle;

% Reset stack using invisible plot
\addplot [forget plot, stack plots=y,draw=none] table [x={#3}, y expr=-(\thisrow{#4}+\thisrow{#5})] {\datatable};
}


%%% macros to make things smalller
% For comparison, the existing overlap macros:
% \def\llap#1{\hbox to 0pt{\hss#1}}
% \def\rlap#1{\hbox to 0pt{#1\hss}}
\def\clap#1{\hbox to 0pt{\hss#1\hss}}
\def\mathllap{\mathpalette\mathllapinternal}
\def\mathrlap{\mathpalette\mathrlapinternal}
\def\mathclap{\mathpalette\mathclapinternal}
\def\mathllapinternal#1#2{%
\llap{$\mathsurround=0pt#1{#2}$}}
\def\mathrlapinternal#1#2{%
\rlap{$\mathsurround=0pt#1{#2}$}}
\def\mathclapinternal#1#2{%
\clap{$\mathsurround=0pt#1{#2}$}}


\usepackage{tikz}
\usepackage{tikzsymbols}
%\usetikzlibrary{external}
%\tikzexternalize[prefix=tikz/]
\usepackage{gnuplot-lua-tikz}


\usetikzlibrary{automata}
\usetikzlibrary{topaths}
\usetikzlibrary{shapes}
\usetikzlibrary{arrows}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{intersections}
\usetikzlibrary{backgrounds}
\usetikzlibrary{positioning}


\tikzstyle{utility}=[diamond,draw=black,draw=blue!50,fill=blue!10,inner sep=0mm, minimum size=8mm]
\tikzstyle{select}=[rectangle,draw=black,draw=blue!50,fill=blue!10,inner sep=0mm, minimum size=6mm]
\tikzstyle{hidden}=[dashed,draw=black,fill=red!10]
\tikzstyle{RV}=[circle,draw=black,draw=blue!50,fill=blue!10,inner sep=0mm, minimum size=6mm]
\tikzstyle{place}=[circle,draw=black,draw=blue!50,fill=blue!20,inner sep=0mm, minimum size=9mm]
\tikzstyle{transition}=[rectangle,draw=black!50,fill=black!20,thick]
\tikzstyle{observed}=[circle,draw=black,draw=blue!50,fill=blue!10,inner sep=0mm, minimum size=6mm]
\tikzstyle{someset}=[circle,draw=black,minimum size=8mm]

\tikzstyle{known}=[rectangle,draw=green!50,fill=green!20,thick]
\tikzstyle{queried}=[rectangle,draw=blue!50,fill=blue!20,thick]
%\tikzstyle{transition}=[rectangle,draw=black!50,fill=black!20,thick]

\tikzstyle{thickarrow}=[->, >=latex, line width=15pt, green!50]
\tikzstyle{medarrow}=[->, >=latex,  line width=5pt]
\tikzstyle{arrow}=[->,>=triangle 60]

\tikzset{every picture/.style={
    line width=1
  }
}

\definecolor{dark-green}{rgb}{0,0.5,0}



%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
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