How can I label terms in an equation using straight lines?

Question

Amsmath and mathtools provides two macros to label terms of an equation:

\documentclass{article}

\usepackage{amsmath}
\usepackage{mathtools}
\usepackage{amsfonts}

\newcommand{\E}[3][]{\mathbb{\operatorname{E}}_{#2}#1[#3#1]}
\newcommand{\KL}[2]{D_\mathrm{\operatorname{KL}}[#1\;\|\;#2]}

\begin{document}

\begin{align}
\underbrace{\E{q_\phi(\theta)}{\ln p(\mathcal{D}|\theta)}}_\text{expected likelihood}
-\underbrace{\KL{q_\phi(\theta)}{p(\theta)}}_\text{complexity} \\
\underbracket{\E{q_\phi(\theta)}{\ln p(\mathcal{D}|\theta)}}_\text{expected likelihood}
-\underbracket{\KL{q_\phi(\theta)}{p(\theta)}}_\text{complexity}
\end{align}

\end{document}

I'd like to get this behavior, except that the brace or bracket is just a thick straight line. Is this possible using these or other packages?

Answer 1

Manipulating the <rule thickness> and <bracket height> in

\underbracket[<rule thickness>][<bracket height>]{<arg>}

suffices. Note that I removed \mathbb{...}, simplified \mathrm{KL}, and changed \;\|\; to \mathrel{\Vert}. You may also want to use \mid instead of | in \ln p(\mathcal{D}|\theta).

\documentclass{article}

%\usepackage{amsmath}
\usepackage{mathtools}
%\usepackage{amsfonts}% not needed since I removed `\mathbb'

\newcommand{\E}[3][]{\operatorname{E}_{#2}#1[#3#1]}
\newcommand{\KL}[2]{D_{\mathrm{KL}}[#1\mathrel{\Vert}#2]}% Put `\mathrm{KL}' in braces. Thanks, @egreg!

\begin{document}

\begin{align}
\underbrace{\E{q_\phi(\theta)}{\ln p(\mathcal{D}|\theta)}}_\text{expected likelihood}
-\underbrace{\KL{q_\phi(\theta)}{p(\theta)}}_\text{complexity} \\
\underbracket{\E{q_\phi(\theta)}{\ln p(\mathcal{D}|\theta)}}_\text{expected likelihood}
-\underbracket{\KL{q_\phi(\theta)}{p(\theta)}}_\text{complexity} \\
\underbracket[0.27778ex][0pt]{\E{q_\phi(\theta)}{\ln p(\mathcal{D}|\theta)}}_\text{expected likelihood}
-\underbracket[0.27778ex][0pt]{\KL{q_\phi(\theta)}{p(\theta)}}_\text{complexity}
\end{align}

\end{document}

I agree with @StevenB.Segletes: This looks rather confusing. Are you dividing the expectation by “expected likelihood”, and dividing the information/entropy by “complexity”? Even with the thick rules, the expressions in Eq. (3) appear to be (poorly typed) fractions at first glance.

Answer 2

You can realize it with other methods than \underbracket:

\documentclass{article}
\usepackage{mathtools}
\usepackage{amssymb}

\newcommand{\E}[3][]{\operatorname{\mathbb{E}}_{#2}#1[#3#1]}
\newcommand{\KL}[2]{D_{\mathrm{KL}}[#1\dmid#2]}
\newcommand{\dmid}{\parallel} % a semantic alias

\newcommand{\explain}[2]{{%
  \vtop{\offinterlineskip\halign{\hfil##\hfil\cr
    $\displaystyle{#1}$\cr
    \noalign{\vskip1pt\hrule height 1pt\vskip1pt}
    {\scriptsize\strut#2}\cr
  }}%
}}

\begin{document}

\begin{equation}
\explain{\E{q_\phi(\theta)}{\ln p(\mathcal{D}\mid\theta)}}
        {expected likelihood}
-\explain{\KL{q_\phi(\theta)}{p(\theta)}\vphantom{\E{q_\phi(\theta)}{}}}
         {complexity}
\end{equation}

\end{document}

I've fixed the definition of \E to have \operatorname and \mathbb switched. There is no need to do \mathrm{\operatorname{KL}} and an additional pair of braces is recommended: D_{\mathrm{KL}} is correct.

A \vphantom will make the underlines align. The | should be \mid.