  Generative Adversarial Networks (GANs) have been impactful on many problems
and applications but suffer from unstable training. The Wasserstein GAN (WGAN)
leverages the Wasserstein distance to avoid the caveats in the minmax
two-player training of GANs but has other defects such as mode collapse and
lack of metric to detect the convergence. We introduce a novel inferential
Wasserstein GAN (iWGAN) model, which is a principled framework to fuse
auto-encoders and WGANs. The iWGAN model jointly learns an encoder network and
a generator network motivated by the iterative primal dual optimization
process. The encoder network maps the observed samples to the latent space and
the generator network maps the samples from the latent space to the data space.
We establish the generalization error bound of the iWGAN to theoretically
justify its performance. We further provide a rigorous probabilistic
interpretation of our model under the framework of maximum likelihood
estimation. The iWGAN, with a clear stopping criteria, has many advantages over
other autoencoder GANs. The empirical experiments show that the iWGAN greatly
mitigates the symptom of mode collapse, speeds up the convergence, and is able
to provide a measurement of quality check for each individual sample. We
illustrate the ability of the iWGAN by obtaining competitive and stable
performances for benchmark datasets.
