  Autoencoders gained popularity in the deep learning revolution given their
ability to compress data and provide dimensionality reduction. Although
prominent deep learning methods have been used to enhance autoencoders, the
need to provide robust uncertainty quantification remains a challenge. This has
been addressed with variational autoencoders so far. Bayesian inference via
MCMC methods have faced limitations but recent advances with parallel computing
and advanced proposal schemes that incorporate gradients have opened routes
less travelled. In this paper, we present Bayesian autoencoders powered MCMC
sampling implemented using parallel computing and Langevin gradient proposal
scheme. Our proposed Bayesian autoencoder provides similar performance accuracy
when compared to related methods from the literature, with the additional
feature of robust uncertainty quantification in compressed datasets. This
motivates further application of the Bayesian autoencoder framework for other
deep learning models.
