Weird placement with align

Question

I want to denote the quantile regression loss, close to the notation in the IQN-paper https://arxiv.org/pdf/1806.06923.pdf (pdf page 3)

I have this code:

\documentclass{book}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}  
\usepackage{amsfonts}
\usepackage{amssymb} 
\usepackage{bbm}

\newcommand{\norm}[1]{\left\lVert #1 \right\rVert}
\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}

\newcommand{\Idf}{\mathbbm{1}} % indicator function
\begin{document}

\begin{align}
    \rho^\kappa_\tau(\delta_{ij}) &= \abs{\tau - \I(\delta_{ij}<0)} \frac{H_\kappa(\delta_{ij})}{\kappa}, \qquad \text{with} \\
    \H_\kappa(\delta_{ij}) &= 
    \begin{cases}
    \frac{1}{2}\delta_{ij}^2 & \text{if} \; \abs{\delta_{ij}} \leq \kappa \\
    \kappa (\abs{\delta_{ij}}-\frac{1}{2}\kappa) & \text{otherwise}
    \end{cases}
\end{align}

\end{document}

Which produces this output:

As can be seen, part of the equations falls of the screen. and the first line of the equation is also placed weirdly, not in the centre of the screen. I tried to remove the \begin{cases} \end{cases} to something simpler and stuff still did not align well so I have the feeling it is due to the align function and not the cases.

Answer 1

When asking about an error it is best to show the error message from the log. The pdf output after any error is possibly useful as a debugging aid but not intended to have sensible layout.

If I fix your errors for \I which is undefined and \H which is a predefined accent then you get

\documentclass{book}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}  
\usepackage{amsfonts}
\usepackage{amssymb} 
\usepackage{bbm}

\newcommand{\norm}[1]{\left\lVert #1 \right\rVert}
\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}

\newcommand{\Idf}{\mathbbm{1}} % indicator function
\begin{document}

\begin{align}
    \rho^\kappa_\tau(\delta_{ij}) &= \abs{\tau - \Idf(\delta_{ij}<0)} \frac{H_\kappa(\delta_{ij})}{\kappa}, \qquad \text{with} \\   
H_\kappa(\delta_{ij}) &= 
    \begin{cases}
    \frac{1}{2}\delta_{ij}^2 & \text{if} \; \abs{\delta_{ij}} \leq \kappa \\
    \kappa (\abs{\delta_{ij}}-\frac{1}{2}\kappa) & \text{otherwise}
    \end{cases}
\end{align}

\end{document}