  The field of neural generative models is dominated by the highly successful
Generative Adversarial Networks (GANs) despite their challenges, such as
training instability and mode collapse. Auto-Encoders (AE) with regularized
latent space provide an alternative framework for generative models, albeit
their performance levels have not reached that of GANs. In this work, we
hypothesise that the dimensionality of the AE model's latent space has a
critical effect on the quality of generated data. Under the assumption that
nature generates data by sampling from a "true" generative latent space
followed by a deterministic function, we show that the optimal performance is
obtained when the dimensionality of the latent space of the AE-model matches
with that of the "true" generative latent space. Further, we propose an
algorithm called the Mask Adversarial Auto-Encoder (MaskAAE), in which the
dimensionality of the latent space of an adversarial auto encoder is brought
closer to that of the "true" generative latent space, via a procedure to mask
the spurious latent dimensions. We demonstrate through experiments on synthetic
and several real-world datasets that the proposed formulation yields betterment
in the generation quality.
