  The rapid advancement of Generative Adversarial Networks (GANs) necessitates
the need to robustly evaluate these models. Among the established evaluation
criteria, the Fr\'{e}chetInception Distance (FID) has been widely adopted due
to its conceptual simplicity, fast computation time, and strong correlation
with human perception. However, FID has inherent limitations, mainly stemming
from its assumption that feature embeddings follow a Gaussian distribution, and
therefore can be defined by their first two moments. As this does not hold in
practice, in this paper we explore the importance of third-moments in image
feature data and use this information to define a new measure, which we call
the Skew Inception Distance (SID). We prove that SID is a pseudometric on
probability distributions, show how it extends FID, and present a practical
method for its computation. Our numerical experiments support that SID either
tracks with FID or, in some cases, aligns more closely with human perception
when evaluating image features of ImageNet data. Our work also shows that
principal component analysis can be used to speed up the computation time of
both FID and SID. Although we focus on using SID on image features for GAN
evaluation, SID is applicable much more generally, including for the evaluation
of other generative models.
