Answers.Body: <blockquote>
  <p>Does the excerpt intend to say that it is practically impossible to evaluate <span class="math-container">$p_g$</span>?</p>
  </blockquote>
  <p>No, this statement says that they <em>assume</em> that they are not going to directly evaluate <span class="math-container">$p_g$</span> for a given problem, and offer other evaluation criteria which does not require doing so, which is the point of the paper. I think the authors have chosen the wording carefully and accurately.</p>
  <p>They have probably been motivated to publish about this approach, because it is not possible to evaluate <span class="math-container">$p_g$</span> in most use cases for GANs. Image generators output highly complex functions with very high dimensionality and a lot of correlation between pixel values. So the paper is of interest <em>because</em> it is hard (usually a practical impossibility) to define <span class="math-container">$p_g$</span> directly, or use something like <a href="https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence" rel="nofollow noreferrer">KL divergence</a> to assess the generator's match to the real distribution.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-09-09T07:47:00.437Z
Answers.LastActivityDate: 2021-09-11T10:43:59.457Z
Answers.LastEditDate: 2021-09-11T10:43:59.457Z
Answers.UserDisplayName: Neil Slater
Body: <p>The following excerpt is taken from <code>3. The Inception Score for Image Generation</code> from the paper titled <a href="https://arxiv.org/pdf/1801.01973.pdf" rel="nofollow noreferrer">A Note on the Inception Score.</a></p>
  <blockquote>
  <p>Suppose we are trying to evaluate a trained generative model <span class="math-container">$G$</span> that
  encodes a distribution <span class="math-container">$p_g$</span> over images <span class="math-container">$\hat{x}$</span>. We can sample from
  <span class="math-container">$p_g$</span> as many times as we would like, <strong>but do not assume that we can
  directly evaluate <span class="math-container">$p_g$</span></strong>. The Inception Score is one way to evaluate
  such a model.</p>
  </blockquote>
  <p>The excerpt is saying that we are not directly evaluating the <span class="math-container">$p_g$</span>, the generator distribution but trying to evaluate the model <span class="math-container">$G$</span>.</p>
  <p>Does the excerpt intend to say that it is practically impossible to evaluate <span class="math-container">$p_g$</span>?</p>
  
Tags: <generative-adversarial-networks><generator>
Title: Is it impossible to evaluate the generator distribution directly?
UserDisplayName: hanugm
ThreadText: # Is it impossible to evaluate the generator distribution directly?
  
  (Asked by: username_0 on 2021-09-09)
  
  The following excerpt is taken from `3. The Inception Score for Image Generation` from the paper titled [A Note on the Inception Score.](https://arxiv.org/pdf/1801.01973.pdf)
  
  > Suppose we are trying to evaluate a trained generative model $G$ that
  > encodes a distribution $p\_g$ over images $\hat{x}$. We can sample from
  > $p\_g$ as many times as we would like, **but do not assume that we can
  > directly evaluate $p\_g$**. The Inception Score is one way to evaluate
  > such a model.
  
  The excerpt is saying that we are not directly evaluating the $p\_g$, the generator distribution but trying to evaluate the model $G$.
  
  Does the excerpt intend to say that it is practically impossible to evaluate $p\_g$?
  
  **Tags:** generative-adversarial-networks, generator
  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2021-09-09. Score: 2
  
  > Does the excerpt intend to say that it is practically impossible to evaluate $p\_g$?
  
  No, this statement says that they *assume* that they are not going to directly evaluate $p\_g$ for a given problem, and offer other evaluation criteria which does not require doing so, which is the point of the paper. I think the authors have chosen the wording carefully and accurately.
  
  They have probably been motivated to publish about this approach, because it is not possible to evaluate $p\_g$ in most use cases for GANs. Image generators output highly complex functions with very high dimensionality and a lot of correlation between pixel values. So the paper is of interest *because* it is hard (usually a practical impossibility) to define $p\_g$ directly, or use something like [KL divergence](https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence) to assess the generator's match to the real distribution.
  
  
  ---
  
  