<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>

CC BY-SA 4.0
2021-09-09T07:47:00.437Z
2021-09-11T10:43:59.457Z
2021-09-11T10:43:59.457Z
Neil Slater
<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>

<generative-adversarial-networks><generator>
Is it impossible to evaluate the generator distribution directly?
hanugm
# 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


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## 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.


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