

\newcommand{\bruno}[1]{{\color{blue}BR:#1}}
\newcommand{\david}[1]{{\color{orange}[DI:#1]}}
\newcommand{\mai}[1]{{\color{red}[ME:#1]}}
\newcommand{\thu}[1]{{\color{teal}[TB:#1]}}

\newcommand{\fullname}{Vertical Validation\xspace}
\newcommand{\name}{VV\xspace}
\newcommand{\measurename}{Better Than Memorization / Generalization Ratio\xspace}


%\newcommand\rs{\bgroup\markoverwith{\textcolor{red}{\rule[0.5ex]{2pt}{0.4pt}}}\ULon}

\newcommand{\Xbase}{\mathbb{X}_{\textnormal{base}}}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\uniq}{uniq}

\newcommand{\held}{\textnormal{held}}

\newcommand{\Xtrain}{\cG_\strain}
\newcommand{\Xtest}{\cG_\sheld}
\newcommand{\Xgen}{\cG_\sgen}
\newcommand{\Xheldw}{\cG_{\sheld,\mathbf{1}}^{(\ell,j)}}
\newcommand{\Gbar}{\bar{G}}

\newcommand{\phideg}{\phi_{ks}^{\textnormal{D}}}
\newcommand{\phiclus}{\phi_{ks}^{\textnormal{C}}}
\newcommand{\phitriads}{\phi_{ks}^{\textnormal{T}}}
\newcommand{\phishort}{\phi_{ks}^{\textnormal{S}}}
\newcommand{\phiclique}{\phi_{ks}^{\textnormal{M}}}

\newcommand{\phimwt}{\phi_{ks}^{\textnormal{Mlwt}}}
\newcommand{\phitpsa}{\phi_{ks}^{\textnormal{TPSA}}}
\newcommand{\phirc}{\phi_{ks}^{\textnormal{RC}}}
\newcommand{\philogp}{\phi_{ks}^{\textnormal{LogP}}}

\newcommand{\phiavg}{\phi_{ks}^{\textnormal{Avg}}}

\newcommand{\pbetamix}{p_\mathrm{BetaMix}}
\newcommand{\qGbar}{q(\Gbar^{(\ell,j)}|\theta = \theta^*_{\Omega(\Xtrain^{(\ell,j)})})}

\newcommand*{\ldblbrace}{\{\mskip-6mu\{}
\newcommand*{\rdblbrace}{\}\mskip-6mu\}}

