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The sentence s "In many supervised learning problems one has an output variable $y$ and a vector of input variables $x$ described via a joint probability distribution $P(x,y)$" from wiki

Here implicitly declared 3 notations $\{x,y,P(x,y)\}$.

So I wonder if there is a math notation so that we can explicitly declare some notation.

For example, we can use @, then s equals to "In many supervised learning problems one has an output variable @ $y$ and a vector of input variables @ $x$ described via a joint probability distribution @ $P(x,y)$", in my personal notebook it's very handy and clear.

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    $\begingroup$ Historically, devices like using italics for such objects to contrast with Roman text, combined with the first appearance, was used. Another was placing such definitions after some highlighted keyword like "Definition". Are you looking for a typeset version, or for something to use in handwritten notes? Gerhard "Calls Dibs On Double Brackets" Paseman, 2019.03.11. $\endgroup$
    – Gerhard Paseman
    Commented Mar 11, 2019 at 14:53
  • $\begingroup$ @GerhardPaseman I want to find some public notation so that I can make myself understood. Personally I want to use in plain text digital notes and handwritten notes. $\endgroup$
    – Voyager
    Commented Mar 11, 2019 at 14:59
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    $\begingroup$ I recommend following textbook conventions for textbooks in your field of study. There is no standard nor a universal convention for this. Gerhard "It Depends Upon The Audience" Paseman, 2019.03.11. $\endgroup$
    – Gerhard Paseman
    Commented Mar 11, 2019 at 15:02
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    $\begingroup$ If you specify their dimensions as well, i.e., $y\in\mathbb{R}^m$, $x\in\mathbb{R}^n$, it is much clearer that they are definitions. It's sort of a clue (and it has the additional benefit that you are clear about their size). There are many similar clues --- italic has been already mentioned, and another is the word let. $\endgroup$
    – Federico Poloni
    Commented Mar 11, 2019 at 17:56

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We may see $:=$ used this way. $$ \text{Let } A_3 := \{n \in \mathbb N\;:\; 3 | n\} $$ That is, let the set of multples of $3$ be denoted by $A_3$.

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  • $\begingroup$ The "walrus operator", as it is known in some circles. $\endgroup$
    – Somatic Custard
    Commented Sep 11, 2020 at 16:24

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