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Regularized Auto-Encoders (RAEs) form a rich class of neural generativemodels. They effectively model the joint-distribution between the data and thelatent space using an Encoder-Decoder combination, with regularization imposedin terms of a prior over the latent space. Despite their advantages, such asstability in training, the performance of AE based models has not reached thesuperior standards as that of the other generative models such as GenerativeAdversarial Networks (GANs). Motivated by this, we examine the effect of thelatent prior on the generation quality of deterministic AE models in thispaper. Specifically, we consider the class of RAEs with deterministicEncoder-Decoder pairs, Wasserstein Auto-Encoders (WAE), and show that having afixed prior distribution, \textit{a priori}, oblivious to the dimensionality ofthe `true' latent space, will lead to the infeasibility of the optimizationproblem considered. Further, we show that, in the finite data regime, despiteknowing the correct latent dimensionality, there exists a bias-variancetrade-off with any arbitrary prior imposition. As a remedy to both the issuesmentioned above, we introduce an additional state space in the form of flexiblylearnable latent priors, in the optimization objective of the WAEs. Weimplicitly learn the distribution of the latent prior jointly with the AEtraining, which not only makes the learning objective feasible but alsofacilitates operation on different points of the bias-variance curve. We showthe efficacy of our model, called FlexAE, through several experiments onmultiple datasets, and demonstrate that it is the new state-of-the-art for theAE based generative models.

To Regularize or Not To Regularize? The Bias Variance Trade-off in Regularized AEs