How to draw a flow chart like this?

Question

I want to have those remarks inside the rectangular box. Thank you so much. So far I made this, but I don't know how to type more words inside the boxes. And how can I make those "Input" cloud and "Output" cloud at the position that I want?

\documentclass{article}
\usepackage[utf8]{inputenc}

\usepackage[latin1]{inputenc}
\usepackage{tikz}
\usetikzlibrary{shapes,arrows}

% Define block styles
\tikzstyle{block} = [rectangle, draw,  
    text width=15em, text centered, rounded corners, minimum height=16em]
\tikzstyle{line} = [draw, -latex']
\tikzstyle{cloud} = [draw, ellipse, node distance=6cm,
    minimum height=8em]

\begin{document}

\begin{tikzpicture}[node distance = 10cm, auto]
    % Place nodes
    \node [block] (init) {\underline{Machine}};
    \node [cloud, left of=init] (data) {\underline{Training data set}};
    \node [cloud, above right of=init] (input) {\underline{Input}};
    \node [cloud, below right of=init] (output) {\underline{Output}};
    % Draw edges
    \path [line] (data) -- (init);
    \path [line] (input) -- (init);
    \path [line] (init) -- (output);
\end{tikzpicture}


\end{document}

Answer 1

As a starting point:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{arrows,
                positioning,    % <--- added
                shapes}
\usepackage{xparse}% So that we can have two optional parameters
\NewDocumentCommand\DownArrow{O{2.0ex} O{black}}%
{%
\mathrel{\tikz[baseline] \draw [<-, line width=0.5pt, #2] (0,0) -- ++(0,#1);}
}
\begin{document}
    \begin{tikzpicture}[
node distance = 3mm and 9mm,
 block/.style = {rectangle, draw, rounded corners,
                 text width =15em, align=center},
 cloud/.style = {draw, ellipse, aspect=1.2, align=center}
                    ]
% Place nodes
\node [block] (init) {\underline{Machine}\
                      $f(\vec{x}) = \theta_0 + \theta_1x_1 + \dotsm + \theta_n x_n$\[1ex]
                      $\DownArrow[30pt]$\[1ex]
                      $y=\phi\bigl(f(\vec{x})\bigr)$
                      };
\node [cloud, left=of init] (data)
                    {\underline{Training data set}\
                     dog, cat, pig, etc};
\node [cloud, above right=of init.east] (input)
                    {\underline{Input}\
                     features data $\vec{x}$};
\node [cloud, below right=of init.east] (output)
                    {\underline{Output}\
                     class: $y$};
% Draw edges
\draw[-latex']  (data) -- (init);
\draw[-latex']  (input) -- (init.east |- input);
\draw[-latex']  (init.east |- output) -- (output);
    \end{tikzpicture}
\end{document}

You were on the right track :). To your code I made the following changes:

• Correct the input encoding (it should be only one, recent article for default use utf8).
• For positioning, use the library positioning and its syntax (note above right=of ... instead your above of = ...).
• The use of \tikzstyle is not recomended. Instead of it, use \tikzset or define styles as options to tikzpicture (as I do in the above MWE).
• After defining align=center, you can write multi line (centered) text in the nodes

edit: next iteration (should be closer to your sketch):

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{arrows,
                positioning,    % <--- added
                shapes}
\usepackage{xparse}% So that we can have two optional parameters
\NewDocumentCommand\DownArrow{O{2.0ex} O{black}}%
{%
\mathrel{\tikz[baseline] \draw [<-, line width=0.5pt, #2] (0,0) -- ++(0,#1);}
}
\begin{document}
    \begin{tikzpicture}[
node distance = 3mm and 9mm,
 block/.style = {rectangle, draw, rounded corners,
                 text width =15em, align=center},
 cloud/.style = {draw, ellipse, aspect=1.2, align=center},
                    ]
% Place nodes
\node [block, label={[anchor=east, align=center, xshift=-1em,
                      font=\small\linespread{0.8}\selectfont, 
                      text=purple]right:
                $x_1,\dotsc,x_n$:\
                 features\ 
                 variables} 
       ] (init) {\underline{Machine}\
                 $f(\vec{x}) = \theta_0 + \theta_1 x_1 + \dotsm + \theta_n x_n$\[1ex]
                 $\DownArrow[30pt]$\[1ex]
                 $y=\phi\bigl(f(\vec{x})\bigr)$
                 };
\node [cloud, left=of init] (data)
                 {\underline{Training data set}\
                  dog, cat, pig, etc};
\node [cloud, above right=of init.east] (input)
                 {\underline{Input}\
                  features data $\vec{x}$};
\node [cloud, below right=of init.east] (output)
                  {\underline{Output}\
                   class: $y$};
% Draw edges
\draw[-latex']  (data) -- (init);
\draw[red,-latex']  (input) -- (init.east |- input);
\draw[red,-latex']  (init.east |- output) -- (output);
    \end{tikzpicture}
\end{document}

Addendum: In the last three years, packages tikz and document class article have undergone several additions, with which the above solution proposal can/had to be now written as follows:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,    % changed
                positioning,    % <--- added
                shapes}
\NewDocumentCommand\DownArrow{O{2.0ex} O{black}}%
{%
\mathrel{\tikz[baseline] \draw [Straight Barb-, semithick, #2] (0,0) -- ++(0,#1);}
}
\begin{document}
    \begin{tikzpicture}[
node distance = 3mm and 9mm,
 block/.style = {rectangle, draw, rounded corners,
                 text width =15em, align=center},
 cloud/.style = {draw, ellipse, aspect=1.2, align=center},
                    ]
% Place nodes
\node [block, label={[anchor=east, align=center, xshift=-1em,
                      font=\small\linespread{0.8}\selectfont,
                      text=purple]right:
                $x_1,\dotsc,x_n$:\
                 features\
                 variables}
       ] (init) {\underline{Machine}\
                 $f(\vec{x}) = \theta_0 + \theta_1 x_1 + \dotsm + \theta_n x_n$\[1ex]
                 $\DownArrow[30pt]$\[1ex]
                 $y=\phi\bigl(f(\vec{x})\bigr)$
                 };
\node [cloud, left=of init] (data)
                 {\underline{Training data set}\
                  dog, cat, pig, etc};
\node [cloud, above right=of init.east] (input)
                 {\underline{Input}\
                  features data $\vec{x}$};
\node [cloud, below right=of init.east] (output)
                  {\underline{Output}\
                   class: $y$};
% Draw edges
\draw[-Latex]  (data) -- (init);
\draw[red,-Latex]  (input) -- (init.east |- input);
\draw[red,-Latex]  (init.east |- output) -- (output);
    \end{tikzpicture}
\end{document}

Result is almost the same as befone: