Is it impossible to evaluate the generator distribution directly?

Question

The following excerpt is taken from 3. The Inception Score for Image Generation from the paper titled A Note on the Inception Score.

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 $p_g$?

Answer 1

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 to assess the generator's match to the real distribution.