Simple algorithm test in latex

algo-test.tex

\documentclass{article}
\usepackage[utf8]{inputenc}
% \usepackage[linesnumbered,ruled]{algorithm2e}
\usepackage{algorithm, algorithmic}
% \usepackage{algorithm,algpseudocode}
% \usepackage{amsfonts}

% ---------- BEGIN of managing indent in algorithm ----------
\newlength\myindent
\setlength\myindent{2em}
\newcommand\bindent{%
  \begingroup
  \setlength{\itemindent}{\myindent}
  \addtolength{\algorithmicindent}{\myindent}
}
\newcommand\eindent{\endgroup}
% ---------- END of managing indent in algorithm ----------

\begin{document}


\begin{algorithm}[H]
  \begin{algorithmic}
  \STATE  \textbf{Input:}
    \bindent
    \STATE \textbullet~ $D$: Training dataset of $n$ data, each with a response variable $y_t$ and a set of variables $X_t$ composed of explanatory covariates $X^{explanatory}$ and categorical covariates $X^{category}$;
    \STATE \textbullet~ $k^*$: pre-defined number of terms;
    \STATE \textbullet~ $criterion()$: performance criterion for a model
    \eindent

  \STATE \textbf{Output:} best fit GAM model in terms of formula containing selected composing terms

  \STATE \textbf{Step 0:} Setting initial values for variables 
  \STATE Let:
    \bindent
    \STATE \textbullet~ $CS_0 = \emptyset$;
    \STATE \textbullet~ $formula = \emptyset$
    \STATE \textbullet~ $criterion = \infty$ {the $criterion$ can be MAPE, ACE, or AIC, etc.}  
    \eindent

  \STATE \textbf{Step 1:} Construction of Candidate Set: $CS_0$ 
  \STATE Adding into $CS_0$ terms of the following forms:
    \bindent
    \STATE \textbullet~ single form: $f(x_{i}^{explanatory})$, 
    \STATE \textbullet~ indexed form: $\sum_{c = 1}^{C}${\bf 1}{($x^{category} = c$)}{$\it f_{c}^{'}(x_{i}^{explanatory})$},
    \STATE \textbullet~ cross form: {$g_{I,~j}$}($x_{i}^{explanatory}$, $x_{j}^{explanatory}$), and 
    \STATE \textbullet~ indexed cross forms $\sum_{c = 1}^{C}${\bf 1}{($x^{category} = c$)}{$\it g_{i, ~j, ~c}^{'}$}{($x_{i}^{explanatory}$, $x_{j}^{explanatory}$)}
    \eindent

  \STATE \textbf{Step 2: }Adding one by one until it exceeds limits or becomes no better 
  \STATE Loop for the $i$-the iteration of adding one new term $t_i$ into the fitting model:
    \bindent
    % 	 \STATE \textbf{For each} $t_i^j \in CS_i$:
    \FOR{each $t_i^j \in CS_i$}
      \STATE find $gam.mod_i^j = gam(y \sim formula + t_i^j)$;
      \STATE find the associated $criterion(gam.mod_i^j)$.
    \ENDFOR
    \STATE Pick $t_i$ as the term $t_i^j$ that yields the best $criterion(gam.mod _i^j)$;
    \STATE also let $criterion_i = criterion(gam.mod _i^j)$
    \STATE Check for termination condition:
    \IF{some condition is true}
      \STATE break from the adding iteration;
    \ELSE
      \STATE $formula = formula + t_i$;
      \STATE $CS_i = CS_{i-1} -\{t_i\}$
    \ENDIF
    \eindent

  \STATE \textbf{Step 3: }output the best fit GAM formula 
  \STATE Best.gam.mod = $formula$

  \end{algorithmic}
\end{algorithm}



% \begin{algorithm}
%   \caption{MyAlgo}
%   \begin{algorithmic}[1]
%     \Statex \textbullet~\textbf{Parameters:} $n, t \in \mathbb{N}$, where $t < n$.
%     \State First step
%     \State Second step
%     \State \ldots
%   \end{algorithmic}
% \end{algorithm}


  
% \begin{algorithm}[H]
% \caption*{my algorithm}
% \begin{algorithmic}
%     \STATE \textbf{Stage one:} this is stage one
%     \bindent
%     \FORALL{i}
%         \STATE do something
%     \ENDFOR
%     \eindent
%     \STATE \textbf{Stage two:} this is stage two
%     \bindent
%     \STATE Update the trie: 
%     \FORALL{j}
%     \STATE do something
%     \ENDFOR
%     \eindent
% \end{algorithmic}
% \end{algorithm}

\end{document}