  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
Markov Chain Monte Carlo (MCMC) sampling has faced several limitations for
large models; however, recent advances in parallel computing and advanced
proposal schemes have opened routes less traveled. This paper presents Bayesian
autoencoders powered by MCMC sampling implemented using parallel computing and
Langevin-gradient proposal distribution. The results indicate that the proposed
Bayesian autoencoder provides similar performance accuracy when compared to
related methods in the literature. Furthermore, it provides uncertainty
quantification in the reduced data representation. This motivates further
applications of the Bayesian autoencoder framework for other deep learning
models.
