\usepackage[show]{chato-notes}
% \newtheorem{theorem}{Theorem}
% \newtheorem{definition}{Definition}
% \newtheorem{problem}{Problem}
% \newtheorem{lemma}{Lemma}

\newcommand{\hide}[1]{}

\newcommand{\expect}[1]{\ensuremath{\mathbf{E}[#1]}}
\newcommand{\prob}[1]{\ensuremath{\mathbf{P}(#1)}}

\newcommand{\expectss}[2]{\ensuremath{\mathbf{E}_{{#1}}[#2]}} % with subscript
\newcommand{\probss}[2]{\ensuremath{\mathbf{P}_{{#1}}(#2)}} % with subscript

% \newcommand{\path}[2]{\ensuremath{\mathit{path}({#1}, {#2})}}
\newcommand{\subtree}[2]{\ensuremath{\mathit{ST}_{#1}({#2})}}
\newcommand{\descendants}[1]{\ensuremath{\mathit{Desc}({#1})}}
\newcommand{\ancestors}[1]{\ensuremath{\mathit{Anc}({#1})}}
% \newcommand{\root}{\ensuremath{\mathit{root}}}

\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator*{\argmax}{arg\,max}

%formating
\newcommand{\spara}[1]{\smallskip\noindent{\bf{#1}}}
\newcommand{\mpara}[1]{\medskip\noindent{\bf{#1}}}
\newcommand{\bpara}[1]{\bigskip\noindent{\bf{#1}}}

\newcommand{\squishlist}{\begin{list}{$\bullet$}
  { \setlength{\itemsep}{0pt}
     \setlength{\parsep}{3pt}
     \setlength{\topsep}{3pt}
     \setlength{\partopsep}{0pt}
     \setlength{\leftmargin}{1.5em}
     \setlength{\labelwidth}{1em}
     \setlength{\labelsep}{0.5em} } }
\newcommand{\squishend}{
\end{list}  }

\newcommand{\transpose}[1]{\ensuremath{{{#1}^{{\mkern-2.5mu\mathsf{T}}}}}}

\newcommand{\failurerate}{\ensuremath{\mathsf{FR}}\xspace}
\newcommand{\sample}{\ensuremath{\mathsf{S}}\xspace}
\newcommand{\human}{\ensuremath{\mathsf{H}}\xspace}
\newcommand{\machine}{\ensuremath{\mathsf{M}}\xspace}
\newcommand{\cfmachine}{\ensuremath{\mathsf{M_{cf}}}\xspace}
\newcommand{\dataset}{\ensuremath{\mathsf{D}}\xspace}
\newcommand{\datasize}{\ensuremath{n}\xspace}
\newcommand{\allFeatures}{\ensuremath{\mathsf{F}}\xspace}
\newcommand{\obsFeatures}{\ensuremath{\mathsf{X}}\xspace}
\newcommand{\obsFeaturesValue}{\ensuremath{x}\xspace}
\newcommand{\leniency}{\ensuremath{\mathsf{R}}\xspace}
\newcommand{\leniencyValue}{\ensuremath{r}\xspace}
\newcommand{\score}[1]{\ensuremath{\mathsf{f}(#1)}\xspace}
\newcommand{\decision}{\ensuremath{\mathsf{T}}\xspace}
\newcommand{\decisionValue}{\ensuremath{t}\xspace}
\newcommand{\humanValue}{\ensuremath{h}\xspace\xspace}
\newcommand{\cfoutcome}{\ensuremath{\hat{\outcome}}\xspace}
\newcommand{\outcome}{\ensuremath{\mathsf{Y}}\xspace}
\newcommand{\outcomeValue}{\ensuremath{y}\xspace}
\newcommand{\doop}[1]{\ensuremath{\mathbf{do}(#1)}}
\newcommand{\unobservable}{\ensuremath{\mathsf{Z}}\xspace}
\newcommand{\unobservableValue}{\ensuremath{z}\xspace}
% \newcommand{\invlogit}{\ensuremath{logit}^{-1}}
\newcommand{\invlogit}{\ensuremath{\sigma}\xspace}
% \newcommand{\logit}{\ensuremath{logit}}
\newcommand{\logit}{\ensuremath{\sigma^{-1}}\xspace}
\newcommand{\parameters}{\ensuremath{\theta}\xspace}
\newcommand{\parameterSpace}{\ensuremath{\Theta}\xspace}
\newcommand{\judgeAmount}{\ensuremath{J}\xspace}

\newcommand{\generalPerformance}{\ensuremath{\mathbf{gp}}\xspace}
\newcommand{\empiricalPerformance}{\ensuremath{\mathbf{ep}}\xspace}
\newcommand{\indicator}[1]{\ensuremath{\delta(#1)}}

\newcommand{\datadistr}[1]{\ensuremath{\mathbf{g}(#1)}\xspace}

\newcommand{\diff}[1]{\ensuremath{\mathsf{d}{#1}}\xspace}
\newcommand{\derivative}[2]{\ensuremath{\frac{\diff{#1}}{{\diff{#2}}}}}

\newcommand{\acomment}[1]{{{\color{orange} [A: #1]}}}
\newcommand{\rcomment}[1]{{{\color{red} [R: #1]}}}
\newcommand{\mcomment}[1]{{{\color{blue} [M: #1]}}}