Answers.Body: <p>In the book you mentioned, the author is dealing with classification, that is, inferring the label <span class="math-container">$y$</span> from a sample <span class="math-container">$x$</span>. Let <span class="math-container">$X$</span> and <span class="math-container">$Y$</span> be the corresponding random variables. <span class="math-container">$p(y|x)$</span> can be understood as <span class="math-container">$P(Y=y|X=x)$</span>, that is, the probability of class <span class="math-container">$y$</span> given that we observed sample <span class="math-container">$x$</span>. Therefore, <strong>for classification</strong>, considering <span class="math-container">$p(x, y) = p(y|x)p(x)$</span> is <strong>more natural</strong> than otherwise.</p>
  
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Answers.CreationDate: 2022-05-30T07:56:39.550Z
Answers.LastActivityDate: 2022-05-30T07:56:39.550Z
Answers.UserDisplayName: Eduardo Montesuma
Body: <p>The probability distribution <span class="math-container">$p(x, y)$</span> can be calculated in two ways :</p>
  <ol>
  <li><span class="math-container">$p(x, y) = p(y \mid x) p(x)$</span></li>
  <li><span class="math-container">$p(x, y) = p(x \mid y) p(y)$</span></li>
  </ol>
  <p>But according to the book <a href="https://books.google.com.np/books/about/Deep_Generative_Modeling.html?id=uidgEAAAQBAJ&amp;printsec=frontcover&amp;source=kp_read_button&amp;hl=en&amp;redir_esc=y#v=onepage&amp;q&amp;f=false" rel="nofollow noreferrer">Deep Generative Modeling</a> (page number 3 first paragraph last line) (1) has clear advantages that (2). Why?</p>
  
Tags: <generative-model><books><probability-theory>
Title: Which formula of p(x, y) to use?
UserDisplayName: Nervous Hero
ThreadText: # Which formula of p(x, y) to use?
  
  (Asked by: username_0 on 2022-05-30)
  
  The probability distribution $p(x, y)$ can be calculated in two ways :
  
  1. $p(x, y) = p(y \mid x) p(x)$
  2. $p(x, y) = p(x \mid y) p(y)$
  
  But according to the book [Deep Generative Modeling](https://books.google.com.np/books/about/Deep_Generative_Modeling.html?id=uidgEAAAQBAJ&printsec=frontcover&source=kp_read_button&hl=en&redir_esc=y#v=onepage&q&f=false) (page number 3 first paragraph last line) (1) has clear advantages that (2). Why?
  
  **Tags:** generative-model, books, probability-theory
  
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  ## 1 answers
  
  ### Answer by username_1 on 2022-05-30. Score: 2
  
  In the book you mentioned, the author is dealing with classification, that is, inferring the label $y$ from a sample $x$. Let $X$ and $Y$ be the corresponding random variables. $p(y|x)$ can be understood as $P(Y=y|X=x)$, that is, the probability of class $y$ given that we observed sample $x$. Therefore, **for classification**, considering $p(x, y) = p(y|x)p(x)$ is **more natural** than otherwise.
  
  
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