  A longstanding problem in machine learning is to find unsupervised methods
that can learn the statistical structure of high dimensional signals. In recent
years, GANs have gained much attention as a possible solution to the problem,
and in particular have shown the ability to generate remarkably realistic high
resolution sampled images. At the same time, many authors have pointed out that
GANs may fail to model the full distribution ("mode collapse") and that using
the learned models for anything other than generating samples may be very
difficult. In this paper, we examine the utility of GANs in learning
statistical models of images by comparing them to perhaps the simplest
statistical model, the Gaussian Mixture Model. First, we present a simple
method to evaluate generative models based on relative proportions of samples
that fall into predetermined bins. Unlike previous automatic methods for
evaluating models, our method does not rely on an additional neural network nor
does it require approximating intractable computations. Second, we compare the
performance of GANs to GMMs trained on the same datasets. While GMMs have
previously been shown to be successful in modeling small patches of images, we
show how to train them on full sized images despite the high dimensionality.
Our results show that GMMs can generate realistic samples (although less sharp
than those of GANs) but also capture the full distribution, which GANs fail to
do. Furthermore, GMMs allow efficient inference and explicit representation of
the underlying statistical structure. Finally, we discuss how GMMs can be used
to generate sharp images.
