\newcommand{\redqueen}{\lr{\textsc{RedQueen}}\xspace}
\newcommand{\cheshire}{\lr{\textsc{Cheshire}}\xspace}
\newcommand{\dataset}{{\cal D}}
\newcommand{\fracpartial}[2]{\frac{\partial #1}{\partial  #2}}
\newcommand{\eg}{\emph{e.g.}}
\newcommand{\ie}{\emph{i.e.}}
\newcommand{\RR}{\mathbb{R}} % Real numbers
\newcommand{\PP}{\mathbb{P}} % Probability
\newcommand{\EE}{\mathbb{E}} % Expectation
\newcommand{\lambdab}{\boldsymbol{\lambda}}
\newcommand{\gammab}{\boldsymbol{\gamma}}
\newcommand{\Ab}{\bm{A}}
\newcommand{\Bb}{\bm{B}}
\newcommand{\Cb}{\bm{C}}
\newcommand{\Db}{\bm{D}}
\newcommand{\Ib}{\bm{I}}
\newcommand{\Mb}{\bm{M}}
\newcommand{\Nb}{\bm{N}}
\newcommand{\Pb}{\bm{P}}
\newcommand{\Ecal}{\mathcal{E}}
\newcommand{\Fcal}{\mathcal{F}}
\newcommand{\Gcal}{\mathcal{G}}
\newcommand{\Hcal}{\mathcal{H}}
\newcommand{\Ncal}{\mathcal{N}}
\newcommand{\Vcal}{\mathcal{V}}
\newcommand{\II}{\mathbb{I}}
\newcommand{\ub}{\bm{u}}
\newcommand{\ib}{\bm{i}}
\newcommand{\diag}{\mathop{\mathrm{diag}}}
\newcommand{\cbr}[1]{\left\{#1\right\}}

% algorithm environment
\renewcommand{\algorithmicrequire}{\textbf{Input:}}
\renewcommand{\algorithmicensure}{\textbf{Output:}}

% colon beginning of algorithm number
\captionsetup[algorithm]{labelsep=colon}

% custom dot
\newcommand*{\Cdot}{\raisebox{-0.45ex}{\scalebox{1.15}{$\cdot$}}}
\newcommand*{\Ldot}{\raisebox{-0.2ex}{\scalebox{1.15}{$\cdot$}}}